Question

which of the following is the equation of an ellipse centered at (2,3) having a horizontal minor axis of length 10 and a major axis of length 12?

Answer 1

i dont know how to start this ...

Answer 2

\[\frac{ x^2 }{ a^2 } + \frac{ y^2 }{ b^2 } = 1 \]

Answer 3

is this the one im suppose to use ??

Answer 4

so the thing i dont get is how do i determine the a and b

Answer 5

This is a great start, although it doesn't go far enough:\[\frac{ x^2 }{ a^2 } + \frac{ y^2 }{ b^2 } = 1\] Please do just a little more research and find the form of this equation of an ellipse that fits an ellipse centered at (h,k).

Answer 6

(2,3) i know x will be (x-2)^2 and y will be (2-3)^2

Answer 7

ok then

Answer 8

oppps i mean y will be (x-3)^2 haha

Answer 9

Look at the original problem statement. It says that the length of the major axis is 12 abd tgat if the minor axis is 10. Hint: major: longer, minor: shorter.

a is HALF of the major axis. We call this the "semi-major" axis, semi- meaning "one half" in this situation. Simlarly, b is HALF of the minor axis and is the "semi-minor axis."

Answer 10

Please re-write your \[\frac{ x^2 }{ a^2 } + \frac{ y^2 }{ b^2 } = 1\] rewriting
\[x^2 ~as~(x-h)^2 ~and\] \[y^2~as~(y-k)^2\]

Answer 11

oh okkkk wait i have a question because in the question it says "horizotal minor axis" this means that this ellipse will be a vertical ellipse right? .... and okk

Answer 12

Suggest that y ou write all this stuff down for later reference.

Yes, I just looked at that myself. If you have a horizontal minor axis, that means you have a vertical major axis, and in turn that means you have a vertical ellipse. Right you are.

Answer 13

Again: ' a ' is the length of the semi-major axis, and ' b ' the length of the semi minor axis. What are a and b in this problem?

Answer 14

\[\frac{ (x-2)^2 }{ b^2 } + \frac{ (y-3)^2 }{ a^2 } = 1 \]

Answer 15

You have correctly positioned a and b based on your knowledge that this is a vertical ellipse. Very nice. So, what is a? What is b? What are \[a^2 ~and~b^2~?\]

Answer 16

ohhhh b=25 and a=36 ???

Answer 17

Yes. So, \[a^2=6^2;~b^2=5^2\]

Answer 18

yay so finally expression will be ....

Answer 19

Actually, no. by 25 you meant b^2; by 36 you meant a^2.

Answer 20

So go ahead now and write what you think the equation of this ellipse is.

Answer 21

\[\frac{ (x-2)^2 }{ 25 } + \frac{ (y-3)^2 }{ 36 } = 1\]

Answer 22

that's great. Notice that you have a larger denom. under the (y-3)^2 term, which is correct because yours is a vertical ellipse. Very nice work. Questions?

Answer 23

no actually im writing this all for reference and future Qs i will encounter today thank you very much for explaning n_n @mathmale

Answer 24

Very much enjoyed working with you! Good luck!