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Q.

If a tangent to the ellipse x2 + 4y2 = 4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point:

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a

3, 0

b

(1, 1) 
 

c

(–1, 1) 
 

d

2,0

answer is A.

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Detailed Solution

Question Image

given ellipse x24+y21=1 

equation of Tangent is 

x2cosθ+y1sinθ=1 is meets  the tangents x=2 & x=-2 at  B2, 1-cosθsinθ C-2, 1+cosθsinθ

equation  of circle B, C as diameter is

 (x-2) (x+2)+y-1-cosθsinθ y-1+cosθsinθ=0 put y=0 x2-4+1=0 x2=3  x=±3

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