Q.

An ellipse has eccentricity 1/2 and a focus at the point P(1/2, 1). One of its directrix is the common tangent  near to the point P, to the circle x2+y2=1 and the  hyperbola x2−y2=1 the equation of the ellipse is

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a

3x2+4y2−6x−8y+4=0

b

3x2+4y2−2x−8y+4=0

c

4x2+3y2−8x−6y+4=0

d

4x2+3y2−8x−2y+4=0

answer is B.

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Detailed Solution

Equation of a common tangent is x = ±1, nearer to  P(1/2,1) is x=1. o the directrix of the ellipse is x = 1 and the focus is  (x−1/2)2+(y−1)2=1/4(1−x)2⇒3x2+4y2−2x−8y+4=0
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