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If the normals at the four points (x_1,y_1),(x_2,y_2),(x_3,y_3) and (x_4,y_4) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 are concurrent. Prove that (x_1+x_2+x_3+x_4)((1/x_1+1/x_2+1/x_3+1/x_4)=4

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