JEE MATHEMATICS MCQ: ELLIPSE

1 Hard

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Analyzing +4 | -1

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

View answer and explanation

Correct option: D

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

Option D is correct because the mean position is derived from the properties of normals to the ellipse and the equation of the ellipse itself.

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