Thread: Ellipses?

Write the equation of the ellipse that meet each set of conditions.

1. The endpoints of the major axis are at (-11,5) (7,5). The endpoint of the minor axis are (-2,9) and (-2,1)

2. The ellipse has center origin a=1 and e=3/4

How would I write these equation I mean for number one I got (2,5) as the center using midpoint formula. But how would I get the denominator in the formula (x-h^2)/a^2 + (y-k^2)/b^2 =1

Originally Posted by homeylova223

Write the equation of the ellipse that meet each set of conditions.

1. The endpoints of the major axis are at (-11,5) (7,5). The endpoint of the minor axis are (-2,9) and (-2,1)

2. The ellipse has center origin a=1 and e=3/4

How would I write these equation I mean for number one I got (2,5) as the center using midpoint formula. But how would I get the denominator in the formula (x-h^2)/a^2 + (y-k^2)/b^2 =1

For 1), the midpoint is (-2, 5). I presume that is a typo. You are given, for example, (-11, 5) and (7, 5) as the major axis. In terms of a how long is the major axis?

-Dan

I mean I meant in the formula I got the (x+2)^2+(y-5)^2 (x-h^2)/a^2 + (y-k^2)/b^2 =1 but for center with midpoint I did get (-2,5)

Would I use the distance formula to find how long the major axis is?

Originally Posted by homeylova223

I mean I meant in the formula I got the (x+2)^2+(y-5)^2 (x-h^2)/a^2 + (y-k^2)/b^2 =1 but for center with midpoint I did get (-2,5)

Would I use the distance formula to find how long the major axis is?

Ummmm...What is (x+2)^2+(y-5)^2 (x-h^2)/a^2 + (y-k^2)/b^2 =1? It looks like part of a circle equation and a general ellipse equation?

Yes, use the distance formula to get the size of the major axis. How do you find a from this number?

-Dan

I got 18 so would A be 9 or half the major axis.

Originally Posted by homeylova223

I got 18 so would A be 9 or half the major axis.

Almost correct. a = 9. And in case that difference seems trivial, Math is case sensitive.

Great! Now how about b?

-Dan

For b I got 4.