If the normal at P on the ellipse x2a2+y2b2=1 cuts the major and minor axes in Q and R respectively then PQ:PR =
A
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B
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C
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D
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Solution
The correct option is D Equation of the normal at P(x1,y1) is a2xx1−b2yy1=a2−b2 Normal cuts major axis at Q(a2−b2a2x1,0) and minor axis at (0,−a2+b2b2y1) Now PQ2=(a2−b2a2x1−x1)2+y21=b4a4x21+y21=b4x21+a4y21a4 PQ2PR2=b4a4⇒PQPR=b2a2