    Question

# A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0,0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is

A
x2+y2=8
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B
x2+y2=34
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C
x2+y2=64
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D
x2+y2=15
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Solution

## The correct option is C x2+y2=64 x225+y29=1; x2+y2=25 P(5cosθ,3sinθ), Q(5cosθ,5sinθ) Equation of normal at Q is y−0=tanθ(x−0) ⇒y=xtanθ Equation of normal at P is 5xcosθ−3ysinθ=16 Solving the two equations, we get y=8sinθ, x=8cosθ x2+y2=64 which represents a circle.  Suggest Corrections  0      Similar questions
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