Question

Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse x²/25 + y²/16 = 1 is equal to 16

Answer 1

Given equation of the ellipse is x²/25 + y²/16 = 1 

Comparing this equation with \(\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1\) 

we get 

a² = 25, b² = 16 

a = 5, b = 4