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JEE Main202311 Apr 2023Evening ShiftMathematicsEllipseActual

If the radius of the largest circle with centre ( 2 , 0 ) inscribed in the ellipse x 2 + 4 y 2 = 36 is r , then 12 r 2 is equal to

Options

  1. A115
  2. B92
  3. C69
  4. D72

Correct answer

B. 92

Step-by-step solution

Given equation of ellipse is x 2 36 + y 2 9 = 1 It is of the form x 2 a 2 + y 2 b 2 = 1 With a = 6 ,   b = 3 . The centre of the circle is C 2 , 0 . Let P a cos θ , b sin θ be the common point for ellipse and circle. P ≡ 6 cos θ , 3 sin θ Equation of normal to the ellipse will be a x cos θ - b y sin θ = a 2 - b 2 . ⇒ 6 x secθ - 3 y cosecθ = 36 - 9 But the normal through P passes through the centre of the circle C 2 , 0 . ⇒ 6 2 secθ - 3 0 cosec&#952

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