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Q.

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 are P and Q is

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a

A circle of radius 2 units

b

 A parabola with focus  as 2,3

c

An ellipse with length of latus rectum is 2 units

d

An ellipse with eccentricity 34

answer is D.

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Detailed Solution

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x2+y2=1,  x2+2y2=4

Rx1,y1 is point of intersection of tangents drawn at P, Q to ellipse PQ chord equation is xx1+2yy14=0 touches x2+y2=112x12+2y12=16     x2+4y2=16  

is ellipse with e=16416=32 

Latus rectum length =244=2

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