Question

If the ecentric angles of the ends of a focal chord of the ellipse x²/a² + y²/b² = 1 (a>b) are  ϴ₁ and ϴ₂ then tan ϴ₁/2 x tan ϴ₂​​​​​/2 equals

Answer 1

The equation of focal chord is given by:

As its a focal chord, it will pass through the focus (ae,0) where e is the eccentricity of the ellipse.

Then, 

Also, the chord could also pass through (−ae,0), thus we can also get the answer as,