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Question

Equation of the locus of the pole with respect to the ellipse x2a2+y2b2=1 of any tangent line to the auxiliary circle is the curve
x2a4+y2b4=λ2 where


A

λ2=a2

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B

λ2=1a2

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C

λ2=b2

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D

λ2=1b2

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Solution

The correct option is B

λ2=1a2


Equation of the auxiliary circle is x2+y2=a2 (i)
Let (h, k) be the pole, then the equation of the polar of (h, k) with respect to the ellipse x2a2+y2b2=1 is
hxa2+kyb2=1 (ii)
Since (ii) is a tangent to circle (i),
1(ha2)2+(kb2)2=±ah2a4+k2b4=1a2Locus of (h,k) is x2a4+y2b4=1a2


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