If the normals at the four points and on the ellipse are concurrent

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the normals at the four points (x1,y1),(x2,y2),(x3,y3)(x_1, y_1), (x_2, y_2), (x_3, y_3) and (x4,y4)(x_4, y_4) on the ellipse x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 are concurrent, then the value of (∑i=14xi)(∑i=141xi)\left(\sum_{i=1}^{4} x_i\right) \left(\sum_{i=1}^{4} \frac{1}{x_i}\right) is

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