Let the normals at the four points (x1,y1),(x2,y2),(x3,y3) and (x4,y4) – InterviewSolution

1.	Let the normals at the four points (x1,y1),(x2,y2),(x3,y3) and (x4,y4) on the ellipse x2a2+y2b2=1 be concurrent at some point (called as conormal point). Then (x1+x2+x3+x4)(1x1+1x2+1x3+1x4) is equal to
Answer» Let 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 $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ be concurrent at some point (called as conormal point). Then $(x_{1} + x_{2} + x_{3} + x_{4}) (\frac{1}{x_{1}} + \frac{1}{x_{2}} + \frac{1}{x_{3}} + \frac{1}{x_{4}})$ is equal to

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