
Equation of an Ellipse
Find an equation of an ellipse satisfying the given conditions.
Foci: (1,6) and (1,0); Length of major axis: 10
Need more of a check on my answer. If it's wrong, then I'll need some explanations on how to do the problem. If right, then that's all I really need.
The center is obviously the midpoint between the 2 Foci, so it's (1,3) and it's vertical.
So it's equation is:
(x+1)^2/b^2 + (y3)^2/a^2 = 1
A is half the length of the major axis (10) so a would = 5.
A squared = 25
C is x in the foci, so it's 1.
C squared = 1
So to find b^2, I need to plug values into:
C^2 = a^2  b^2
1=25b^2
b^2 = 24
So, assuming all of the above is correct, the final equation should be:
(x+1)^2/24 + (y3)^2/25 = 1
Correct? Thanks.

Hello, IAmLegendToo!
is the distance from the center to a focus: .
Give it another try . . .

Ahh, that sounds more correct. I don't know why I thought of it as simply X in a foci. Hmm.
So then it's:
C=3
C^2 = 9
9 = 25  b^2
b^2 = 16
b= 4
So, then equation would be:
(x+1)^2/16 + (y3)^2/25 = 1
Correct now?