If the points of intersection of the ellipse x 2 16 + y 2 b 2 = 1 and the circle x 2 + y 2 = 4 b , b 4 lie on the curve y 2 = 3 x 2 , then b is equal to :

Question

If the points of intersection of the ellipse x 2 16 + y 2 b 2 = 1 and the circle x 2 + y 2 = 4 b , b > 4 lie on the curve y 2 = 3 x 2 , then b is equal to :, 12, 5, 6, 10

MARKS App · Accepted Answer

y 2 = 3 x 2 and x 2 + y 2 = 4 b Solving both the equations we get, x 2 = b As x 2 16 + y 2 b 2 = 1 ⇒ x 2 16 + 3 x 2 b 2 = 1 ⇒ b 16 + 3 b = 1 ⇒ b 2 - 16 b + 48 = 0 ⇒ b - 12 b - 4 = 0 ⇒ b = 12 ∵ b > 4

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