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Question

If a variable tangent of the circle x2+y2=1 intersect the ellipse x2+2y2=4 at P and Q then the locus of the points of intersection of the tangents at P and Q is

A
A circle of radius 2 units
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B
A parabola with fouc as (2, 3)
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C
An ellipse with eccentricity 34
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D
An ellipse with length of latus rectrum is 2 units
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Solution

The correct option is D An ellipse with length of latus rectrum is 2 units
x2+y2=1; x2+2y2=4
Let R(x1,y1) is point of intersection of tangents drawn at P,Q to ellipse PQ is chord of contact of R(x1,y1)
xx1+2yy14=0
This touches circle r2(l2+m2)=n21(x21+4y21)=16x2+4y2=16 is ellipse with eccentricity e=32 and length of latus rectum LL1=2

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