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If the tangent at on the ellipse
touches the circle then
detailed solution
Correct option is C
Centre of the circle is (– 1, 0) and radius is 4. Equation of the tangent at P(θ) to the ellipse isx4cos θ+y16/11sin θ=1If this touches the circle, then−cos θ4−1cos2 θ16+sin2 θ256/11=4⇒(cos θ+4)2=256cos2 θ16+11sin2 θ256⇒4cos2 θ−8cos θ−5=0⇒(2cos θ−5)(2cos θ+1)=0⇒cos θ=−1/2⇒θ=2π/3Talk to our academic expert!
Similar Questions
Let P be any point on the directrix of an ellipse of eccentricity e. S be the corresponding focus and C the centre of the ellipse. The line PC meets the ellipse at A. the angle between PS and tangent at A is , then is not equal to
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