Question #2f37e

1 Answer
Mar 16, 2016

#x^2+2y^2 = a^2#.

Explanation:

The #triangle F1TF2 is isosceles, with F1T =- F2T = semi-major axis a..

F1F2 = 2ae, where e is the eccentricity of the ellipse,

The altitude from T = the semi-minor axis b = a#sqrt(1-e^2)#

F1P + F2P = 2a, for any point P on the ellipse.

Here, #angle# F1F2T = 45 deg.
So e = #1sqrt2#.
b = #a/sqrt2#.