The normals at four points on the ellipse x^2/a^2 + y^2/b^2 = 1 meet in the point (h, k). Then the mean position of the four points is ​

Question

The normals at four points on the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2 } = 1\) meet in the point (h, k). Then the mean position of the four points is

(a) \(\left(\frac{a^2h}{2(a^2 + b^2)}, \frac{b^2k}{2(a^2 + b^2)}\right)\)

(b) \(\left(\frac{a^3h}{2(a^2 + b^2)}, \frac{b^3k}{2(a^2 + b^2)}\right)\)

(c) \(\left(\frac{ah}{2(a^2 - b^2)}, \frac{bk}{2(a^2 - b^2)}\right)\)

(d) \(\left(\frac{a^2h}{2(a^2 - b^2)}, \frac{b^2k}{2(a^2 - b^2)}\right)\)

Answer 1

Correct option is (d) \(\left(\frac{a^2h}{2(a^2 - b^2)}, \frac{b^2k}{2(a^2 - b^2)}\right)\)