Question

Length of focal chord of an ellipse when one of its endpointsos given?

Answer 1

1)If the end points are given as (X,Y) and as it is focal chord, it will be passing through the one of the foci of the ellipse (x²/a²)+(y²/b²)=1 i.e. (ae,0) where e is eccentricity of the ellipse.

2) Find the equation of the focal chord by using both points by using the two-point line equation.

3)After finding equation of line just find out the points at which it intersects the ellipse, after getting coordinates of the another point other than the given one, use distance formulae to calculate distance between them.

USE VALUES TO UNDERSTAND BETTER, BUT GENERAL WAY OF SOLVING IS THE SAME, PROBABLY NOT THE SHORTEST BUT CORRECT