The locus of midpoints of a focal chord of the ellipse x^2/a^2 + y^2/b^2 = 1 is ​

Question

The locus of midpoints of a focal chord of the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} =1\) is

(a) \(\frac{x^2}{a^2} + \frac{y^2}{b^2} =\frac{ex}a\)

(b) \(\frac{x^2}{a^2} - \frac{y^2}{b^2} =\frac{ex}a\)

(c) x² + y² = a² + b²

(d) None of these

Answer 1

Correct option is (a) \(\frac{x^2}{a^2} + \frac{y^2}{b^2} =\frac{ex}a\)