How do you find

how do you find the center of a parabola and if it doesnt have a center why not?

Example:
#24
y+4=1/8(x-2)^2

Study Guide

On the study guide...

Chapter 3, #3(free response), #12 b & #16
Yeah, I don't know how to do any of those...any help?

?

Does circles have a major or minor axis? if so how do you find them?
and do they have a vertex and focus? What can a circle have?

Reflection #7.

Well, i'm happy to say that i didn't struggle at all this week!
:)

one thing i really know well now is circles, i'll just try to explain these:

Equation of a circle in standard form is:
(x-h)^2+(y-k)^2=r^2
center(h,k) radius(r)

If not in standard form, you must complete the square to put into standard form.

If given the center and a point, you can use the distance formula to find the radius.

To find the intersection of a line and a circle:
first, solve for y.
second, substitute it in your circle equation.
third, solve for x.
fourth, plug y in to get y.

NOTE: if your x-value is imaginary there is NO INTERSECTION.

Ex:
Find center and radius:

1. (x-3)^2+(y+7)^2=19
center: (3, -7) radius: (square root of 19)

2. PUT IN STANDARD FORM TO FIND CENTER AND RADIUS:
x^2+y^2+16x-12y+5=0
COMPLETE THE SQUARE:
x^2+16x+y^2-12y=-5
x^2+16x+64+y^2-12y+36=-5+64+36
(x+8)^2+(y-6)^2=95
CENTER:(-8,6) radius: (square root of 95)



one thing i still am a little "iffy" about is the graphing of ellipses.
my notes were a little confusing and i'm still having issues with the two ways to find foci, do we use both or are they simply options?
PLEASE HELP! :)

Reflection #7

Graphing an ellipse was the easiest thing for me..

The formula is:
(x-h)^2/(length of x/2)^2+(y-k)^2/(length of y/2)^2=1

1. center: (h,k)

2. major axis: larger denominator

3. vertex: on major axis; +/- square root of small denominator

4. find focus: smaller # or denominator^2=larger # or denominator^2-focus^2

5. length of major axis 2 square root of larger denominator

6. length of minor axis 2 square root of smaller denominator

then graph...

I'm having a little trouble with the chapter 6 test on the inverses..

Reflectin 7

This week was not too bad. Since everyone seems to be reviewing ellipses, I guess i will do a review on hyperbolas. First off the equation of a hyperbola in standard form is (x-h)^2/(length/2)^2-(y-k)^2/(length/2)^2=1 or -(x-h)^2/(length/2)^2+(y-k)^2/(length/2)^2=1. The center of a hyperbola is (h,k). The major axis is non-negative denominator. The minor axis is 2 times the square root of the negative denominator. The vertex is plus or minus the square root of the non negative denominator. (vertex is on the major axis). The asymptotes are y=plus or minus the square root of the y denominator/x denominator times x and must be in "slope intercept" form (y=mx+b) To find the formula(c^2) you use the formula c^2=x denominator+y denominator.

Now one thing I don't get is the length of the major and minor axis. Is it the same as an ellpise where the length of the axis is 2 times the square root of the denominator?

Reflection #7

This week was really easy. I think that circles are the easiest thing in math, so far. Standard form is really simple. (x-h)^2+(y-k)^2=r^2. If it is not in standard form, you have to complete the square to get it in standard form. The center of the circle is (h,k) and the radius is (r).

EX:

(x-8)^2+(y+2)^2=36

center (8,-2)
radius = 6


_____________________________________________________________

To find the intersection of a line and a circle:

1) Solve the linear equation for y.

2) Substitute in circle equation.

3) Solve for x.

4) Plug x value in to get y value.

**If your x value is imaginary, then there is no point of intersection**

__________________________________________________________

To graph the cirlce in your calculator:


Go to the Y= button, plug the equation in positive and then negative (if there is a gap, close it when you draw it on the paper)


___________________________________________________________

Overall, this week was pretty easy. I just don't understand ellipses all that well, but i hope that i will catch on this week!

Reflection 7

This week was an overall good one. We learned conics and ellipses. I didnt think the stuff we learned was to hard its just trying to remember all of the steps i'm also worried about the exam as little cause its gonna be on so much stuff but hopefully i should do all right. This week i went to LHS and got ass raped ny a bunch of asains in a math competiton. Wasn't my best day either. To day, howeva we went have a little get together and started working on our take home test, and i think we are doing well, but DOES ANYONE HAVE ANY IDEA WHAT A DIRECTRIX IS?
I do understand how to solve an ellipse, here are the steps:
(x-h)^2/(length of x/2)^2+(y-k)^2/(length of y/2)^2=1Center = (h,k)Major Axis = Larger DenominatorVertex is on the Major AxisFocus = smaller # or denominator^2=larger # or denominator^2-focus^2a)Find centerb)Major axis-bigger denominator x or yc)Vertex + or - square root of big denominatord)Other integer + or- square root of small denominatore)Find Focusf)Length of major axis 2 square root of big denominatorg)Length of the minor axis 2 square root of small denominatorh)Graph

reflection 7

This week was just another week. It wasn't that hard, some things i got and some things i didn't. No big deal. It went by pretty fast, since we had a four day week:)

Here's an example of a ellipse...

x^2/25+y/1=1


1. center (0,0)
2.major axis is the x-axis
3.minor axis is the y-axis
4.vertex is (5,0) (-5,0)
5.other denominator is (1,0) (-1,0)
6.the focus is (2 square root of 6, 0) (-2 square root of 6,0)
7.length of major axis 2(square root of 25)=10
8.length of minor axis 2(square root of 1)=2
9.graph..obviously can't do that on here..

Reflection # 7

This week I picked up on ellipses the best. The first thing you need to do with an ellipse is make sure the equation is equal to one. If it is not, divide the entire equation by that number to get the eqn. equal to one.

Then check for the center.
if the x^2 and y^2 terms are numerators by themself, the center is (0,0)

Then foolow the steps given in the notes, they will explain everything. I would list them, but I didnt quite memorize them yet and I forgot my notebook at school so I dont wanna accidentally tell you guys the wrong thing. But the steps are really clear and if you know them like the back of your hand you will have no problems with ellipses.
_____________________________________________________________

I did not understand the whole thing with the hyperbolas.

reflection #7

this week was pretty fast, because of the field trip on thursday... but we did learn about conic sections

to graph an ellipse
(x-h)^2/(length of x/2)^2+(y-k)^2/(length of y/2)^2=1

center: (h,k)
major axis: larger denominator
vertex: on major axis; +/- square root of small denominator
find focus: smaller # or denominator^2=larger # or denominator^2-focus^2
length of major axis 2 square root of larger denominator
length of minor axis 2 square root of smaller denominator
graph

i understand this stuff, but hyperbolas are killing me

reflection 7

another fast week goes by, and we learned about ellipses,conic sections, and hyperbolas

ellipse: X^2 + y^2 =1
9 4


hyperbola: x^2 - y^2
16 49

both are pretty easy to understand and graph, and im not having any current problems with this

reflection 7

So this week went by fast in school! But we still learned alot about the conic sections. And thanks b-rob for all this stuff your given us to do, i really appreciate it. We learned how to graph ellipses, circles and hyperbolas. Ellipses are my favorite.

these are the steps to graph ellipses:
(x-h)^2/(length of x/2)^2+(y-k)^2/(length of y/2)^2=1
Center = (h,k)
Major Axis = Larger Denominator
Vertex is on the Major Axis
Focus = smaller # or denominator^2=larger # or denominator^2-focus^2


a)Find center
b)Major axis-bigger denominator x or y
c)Vertex + or - square root of big denominator
d)Other integer + or- square root of small denominator
e)Find Focus
f)Length of major axis 2 square root of big denominator
g)Length of the minor axis 2 square root of small denominator
h)Graph

Hyperbolas are what gets me!
I dont know how to get the asymptotes (i dont even know what that is)

HELP!!!!

how do you find the directrix of hyperbola???
on number of 20 of the chapter 6 test.

Reflection 7

Okay. This week wasn't that bad at all. With the field trip on Thursday we still managed to get a lot of information into the lesson plan. In class this week, we learned all about conic sections. I remember circles, ellipses, and hyperbolas. But I will describe how to do ellipses for you people.

There are many elements of an ellipse:

The equation: ((x-h)^2/(length of x/2)^2) + ((y-k)^2/(length of y/2)^2)

Center: (h, k)

Major axis has the larger denominator

Vertex is on major axis

focus: smaller # = larger # - focus^2

focus is on major axis, also

How to graph:

1. center

2. major axis - bigger demoninator x or y

3. vertex is plus or minus sqrt of big denominator

4. other intercepts is plus or minus sqrt of small denominator

5. focus

6. length of major axis is 2 times the sqrt of big denominator

7. length of minor axis is 2 times the sqrt of small denominator

8. then graph it

The only thing i really don't understand is what the lengths of the major and minor axis pertain to?

reflection 7

woohoo, another week is over, and another begins :/..... anyway, this week was pretty easy and good. Not too much schoolwork though. I mean, we had that field trip, and gettin ready for saturday and a whole bunch of stuff. Saturday was pretty good during the day, but after we got back, it was pretty awesome. The party was really fun, especially the movie game and the countless games of mafia :D. Anyway.....i dont really have time to ramble on and on and on like always.....soo.....
back to math

i did understand how to do stuff like sketchin ellipses

x^2/25+y/1=1

so the center is (0,0), the major axis is the x axis,
the vertex is ±√the bigger denominator, so its (5,0)(-5,0)
the other intercepts are ±√the other denominator, so its (1,0)(-1,0)
the focus is (smaller denominator)^2=(larger denom)^2-focus^2, so c=±2√6, so the foci are (2√6,0)(-2√6,0)
length of the major axis is 2(√the bigger denom), so the length of the major axis is 2(√25)=10
length of the minor axis is 2(√the smaller denom), so the length of the minor axis is 2(√1)=2
then u just graph it w/ all the information in the problem

but one thing i need help is w/ the hyperbolas, like how to find the asymptotes and stuff

Reflection 7

This week went fast but it wasn't the easiest. I have to start doing my take home test that looks real hard. And I am about to do my powerpoint presentation for monday. Brob also gave us a bunch of packets, but at least we are doing those in class.

Here are the steps for Ellipses:

1. center

2. major axis-bigger denom x or y

3. Vertex + or - square root of big denom.

4.Other int. + or- square root of small denom.

5. Focus

6. length of major axis 2 square root of big denom.

7. length of the minor axis 2 square root of small denom.

8. Graph
________________________________________
I dont exactly know how to do hyperbolas when it gets to step 6, 7, and 8. The focus part.

Reflection 7

I understood how to do everything we learned this week. But I found ellipses to be easier. And they are easier to explain.

1. (x-h)^2/(length of x/2)^2+(y-k)^2/(length of y/2)^2=1
2. (h,k) center
3. Major axis has the larger denominator
4. vertex is on major axis
5. focus: smaller # or denominator^2=larger # or denominator^2-focus^2
-Focus is on major axis.

To sketch.
1. Find center
2. Major axis=bigger denominator x or y
3. vertex +/- Square root of bigger denom.
4. other intercept +/- Square root of smaller denom.
5. focus (refer back to #5 at top)
6. length of major axis 2 square root of bigger denom.
7. length of minor axis 2 square root of smaller denom.
8. graph

Sketch-

x^2/25+y/1=1

1. (0,0)
2. x-axis is major
3. (5,0)(-5,0)
4. (0,1)(0,-1)
5. 1=25-c
c= +/- square root of 24
= +/- 2 Square root of 6
= (2 Square root of 6,0) (-2 Square root of 6,0) <---Plot (foci)
6. 2(Square root of 25)= 10
7. 2(Square root of 1)=2
8. Graph
------------------------------
I still don't get anything about the time and stuff we learned in the last chapter.

REFLECTION #7

So this week went by suuupppeeerr fast!!! :) And I was so excited that we didn't have any quizzes either! But not so excited about that Chapter 6 take home test. That should be fun to do! But I have to say, class on Thursday was such a relief for me. Since the whole class, except me and three other people, was on the field trip, it gave us a little break from all the learning we do in that class. :P hah. Well anyway, this week we learned about conics. Basically, we learned the equation of a circle, and also how to find the intersection of a line and a circle. Then we learned about ellipses and hyperbolas. I used to get confused between those two things but now I can recognize the difference between them easily. Ellipses are all positive while somewhere in a hyperbola there is a negative. Sooooo.. for the most part I pretty much caught on to everything we went over this week. The steps are easy to follow, I just have to fully memorize all of them to make my life less complicated. All this stuff should come easy to me once I get the hang of it.

Anyway, what I thought were the easiest things we learned this week was finding the center and radius of circles, writing in standard form, and finding the intersection of circles.


So here are some examples of each of those things:

Ex. 1.) Find the center and radius of the circle.
(x+4)^2 + (x-9)^2 = 9
Radius>> square root of 9 >>> equals 3
Center>> (h,k) >> (-4,9)


Ex. 2.) Write in standard form.

x^2 + y^2 - 2x - 8y + 16 = 0
x^2 - 2x + ____ + y^2 - 8y + ____ = -16 >> (get all x's together and y's together..)
(..use completing the square)
x^2 - 2x + 1 + y^2 - 8y + 16 = -16 + 1 + 16 >> (* -2/2 squared = 1 , and -8/2 squared = 16..)
(..add 1 and 16 after equal sign also)

standard form>> (x-1)^2 + (y-4)^2 = 1


Ex. 3.) Find the intersection of the circle.

x^2 + y^2 = 25 y = 2x -2

*Okay the first thing you want to do is solve the linear equation for y.

**it's already solved for y.>>> y = 2x -2

*Now you substitute the linear equation into the circle equation:

x^2 + (2x-2)^2 = 25

*Solve for x:

x^2 + (2x-2)^2 = 25
x^2 + 4x^2 - 8x + 4 = 25
5x^2 - 8x + 4 = 25
5x^2 - 8x - 21 = 0
(5x^2 - 15x) + (7x - 21) = 0
5x(x-3) + 7(x-3) = 0
(5x + 7) (x - 3)
x = -7/5 x = 3

*Now you plug in the x values into your linear equation to get the y values:

2(3) - 2 = 4 >>> (3,4)
2(-7/5) - 2 = -24/5 >>> (-7/5, -24/5)

Final answers are (3,4) and (-7/5, -24/5)


Now for what I didn't quite understand at all this week. I didn't get how to graph a circle on my calculator. Well, I can graph it, I just can't do the little thing when you have to press the arrows and make the little dot go all over the place on the graph. (sorry I don't know what it's called :/ ) So yeah I'd rather not attempt this on my calculator by myself, because I'd probably end up breaking it. Not going to take any chances on that, hah. So please please if anyone can help me that would be so great :)

Overall, I thought this week was a good week. I think we learned everything at a good pace.

Reflection 7

This week we learned about Ellispes and Hyperbolas. Im still a little confused on ellispes and how to "FIND THE EQUATION OF THE eLLISPES WITH A VERTEX (0,-8) AND A MINOR AXIS SIX UNITS LONG"

Solving hyperbolas you first have to know the step and eqautions to solve and graph it....

1. (x-h)^2 / (length/2)^2 - (y-k)^2 / (length/2)^2=1 OR -(x-h)^2 / (length/2)^2 + (y-k)^2 / (Length/2)^2 =1

2.Center(h,k)

3.major axis non-negative

4.vertex +/- the sqaure root of "non-negative denom."

5.asymptotes y=-/+ the sqaure root of "y denom." over the square root of "x denom."

6.focus^2= x denom. + y denom.
focus^2= vertex^2 + other denom.

Example: x^2/36 - y^2/9 =1
1. Hyperbola bc of the minus sign
2. the center is (0,0)
3. x axis bc its not neg.
4. y axis bc its neg.
5.none
6.c^2= 36+9
c^2= 45
c= +/- square root of 45
c= 3 square root of 5
7. y=+/- sqaure root of 9 over sqaure root of 36(x)=(y= 1/2x)


Then you graph it

Reflection #7

alright this week we learned how to find circles, ellipses, and hyperbolas. the thing that i understood the most from this week would have to be ellipses here are some examples for ellipses:

x^2/25 + y^2/1 = 1

1. first you find the center
(0,0)

2. find the major axis
x-axis

3.find the vertex
(5,0)(-5,0) on the x-axis

4. find the other intersept
(0,1)(0,-1)

5. find the focus
1= 25-c^2
c= +/- square root 24
c= +/- 2 square root 6
(-2 square root 6, 0)(2 square root 6,0)

6. find the length of the major axis
2(square root of 25)
=10

7. find the length of the minor axis
2(square root of 1)
=2

8. now you graph.
step 3 and 4 you graph this
step 5 you plot.


now something i didn't quite get was hyperbolas i didn't understand how to find the asymptotes and graph them..help please