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JEE Main202131 Aug 2021Evening ShiftMathematicsParabolaActual

A tangent line L is drawn at the point 2 , - 4 on the parabola y 2 = 8 x . If the line L is also tangent to the circle x 2 + y 2 = a , then a is equal to .

Correct answer

0

Step-by-step solution

Given, Parabola y 2 = 8 x and circle x 2 + y 2 = a 2 Parabola y 2 = 8 x at point 2 , - 4 Differentiating w .r. t. x ' ' 2 y d y d x = 8 d y d x = 4 y d y d x 2 , - 4 = - 1 Equation of tangent y - y 1 = d y d x x - x 1 y + 4 = - 1 x - 2 x + y + 2 = 0 Line L is also tangent to the circle x 2 + y 2 = a 2 So, O A = a at 0 , 0 1 × 0 + 1 × 0 + 2 2 = a 2 = a ⇒ a = 2

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