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# Equations of ellipse

What is the equation of the ellipse with foci at (0,-3) and (0,3) and the sum of focal radii being 10?

I tried it two different ways and am not sure if either is correct:
First way:
2a=10 so a=5 (sum of focal radii)

Center is (0,0) halfway between foci

c=3

b^2=a^2-c^2 or b^2 = 16

giving me the equation x^2/16 + y^2/25 = 1

Then I tried it like the textbook by using the distance formula:
squareroot of [x² + (y+3)²] + squareroot of [x² + (y-3)²]=10
When I tried to square both sides, I ended up getting it simplified to x²+y²= 41

Obviously totally different answers—not sure which is correct and why the other is incorrect.

first you can not square both sides as easy as that ans second The first equation is
(x2/25) + (Y2/16) = 1
16x2 + 25y2 = 400