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Q.

If tangents PQ and PR are drawn from a point on the circle  x2 + y2 = 25 to the ellipse x24+y2b2=1,(b<4),  so that the fourth vertex S of parallelogram PQSR lies on the circumcircle of triangle PQR, then eccentricity of the ellipse is

 

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a

54

b

73

c

74

d

53

answer is C.

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Detailed Solution

Equation of the ellipse is x216+y2b2=1   ….(1)
Equation of the circle is x2 + y2 = 25 ..... (2)
If PQSR is a square or rectangle then QPR=90°
(2) is a director circle of (1)
16 + b2 = 25  b = 3

For ellipse a2=16,b2=9 Now e=a2-b2a2=74

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