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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 ( x 1 , y 1 ) , ( x 2 , y 2 ) , ( x 3 , y 3 ) (x_1, y_1), (x_2, y_2), (x_3, y_3) ( x 1 , y 1 ) , ( x 2 , y 2 ) , ( x 3 , y 3 ) and ( x 4 , y 4 ) (x_4, y_4) ( x 4 , y 4 ) on the ellipse x 2 a 2 + y 2 b 2 = 1 \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 a 2 x 2 + b 2 y 2 = 1 are concurrent, then the value of ( ∑ i = 1 4 x i ) ( ∑ i = 1 4 1 x i ) \left(\sum_{i=1}^{4} x_i\right) \left(\sum_{i=1}^{4} \frac{1}{x_i}\right) ( ∑ i = 1 4 x i ) ( ∑ i = 1 4 x i 1 ) is
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