The locus of the image of the focus of the ellipse x225+y29=1 with respect to any of the tangents to the ellipse is
A
(x+4)2+y2=100
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B
(x+2)2+y2=50
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C
(x−4)2+y2=100
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D
(x−2)2+y2=50
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Solution
The correct options are A(x+4)2+y2=100 C(x−4)2+y2=100 Equation of the ellipse is x225+y29=1 Foci (±4,0) Let S′(h,k) be the image. Mid point of SS′ is M≡(h±42,k2) SS′ cuts tangent line at point M which lies on the auxiliary circle of the ellipse , since foot of perpendicular from foci upon any tangent lies on auxilary circle. Auxiliary circle of the ellipse is x2+y2=25 ∴M lies on auxiliary circle. So, ⇒(h±42)2+k24=25 ∴ Required locus equation is (x±4)2+y2=100