Question

Question #2f37e

Answer 1

`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`.