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Question

How many tangents to the circle x2+y2=3 are there which are normal to the ellipse x29+y24=1

A
3
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B
2
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C
1
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Solution

Equation of normal at p(3cosθ,2sinθ) is 3xsecθ2ycosecθ=5
59sec2θ+4cosec2θ=3But minimum value of 9sec2θ+4cosec2θ=25no such θ1 exists
So the number of tangents to the circle x2+y2=3 which are normal to the ellipse x29+y24=1 is 0.

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