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# If the tangent at θ on the ellipse x2a2+y2b2=1 meets the auxiliary circle at two points which subtend a right angle at the centre, then e2(2−cos2θ)=

A
1
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B
2
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C
1
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D
0
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Solution

## The correct option is A 1Homogenising the equation of the auxiliary circle x2+y2=a2 with the help of the tangent at θ i.e., xacosθ+ybsinθ=1, we get x2+y2−a2(xacosθ+ybsinθ)2=0 Since this equation represents a pair of perpendicular, lines, we have sum of the coefficients of x2 and y2 is zero ⇒(1−cos2θ)+1−a2b2sin2θ=0⇒b2sin2θ+b2−a2sin2θ=0⇒a2(1−e2)(1+sin2θ)−a2sin2θ=0 ⇒(1−e2)(1+sin2θ)=sin2θ On simplification, we get, e2(2−cos2θ)=1  Suggest Corrections  0      Similar questions
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