If the points of intersection of the ellipse x 2 16 + y 2   b 2 = 1 and the circle x 2 + y 2 = 4  …

If the points of intersection of the ellipse x216+y2 b2=1 and the circle x2+y2=4 b, b>4 lie on the curve y2=3x2, then b is equal to :

  1. 12
  2. 5
  3. 6
  4. 10

Solution

y2=3x2 and x2+y2=4b

Solving both the equations we get, 

x2=b

As x216+y2b2=1

⇒x216+3x2b2=1

⇒b16+3b=1

⇒b2-16b+48=0

⇒b-12b-4=0

⇒b=12 ∵b>4

Asked in: JEE Main 2021 (16 Mar Shift 2)

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