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JEE Main202225 Jul 2022Morning ShiftMathematicsParabolaActual

The sum of diameters of the circles that touch (i) the parabola 75 x 2 = 64 5 y - 3 at the point 8 5 , 6 5 and (ii) the y -axis, is equal to _____ .

Correct answer

0

Step-by-step solution

Given, x 2 = 64 × 5 75 y - 3 5 Now equation of tangent at 8 5 , 6 5 will be given by, x × 8 5 = 64 15 y + 6 5 2 - 3 5 ⇒ 3 x - 4 y = 0 Now equation of family of circle will be, x - 8 5 2 + y - 6 5 2 + λ 3 x - 4 y = 0 ⇒ x 3 + y 3 + x 3 λ - 16 5 + y - 4 λ - 12 5 + 4 = 0 It touches y axis so 2 f 2 - c = 0 ⇒ f 2 = c So, 4 λ + 12 5 2 4 = 4 ⇒ λ = 2 5 or λ = - 8 5 If, λ = 2 5 ,   then  r = 1 And if λ = - 8 5 ,   then   r = 4 Now s

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