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JEE Advanced2015MathematicsParabolaActual

If the normal of the parabola y 2 = 4 x drawn at the end points of its latus rectum are tangents to the circle x - 3 2 + y + 2 2 = r 2 , then the value of r 2 is

Correct answer

0

Step-by-step solution

End points of latus rectum A ( 1 , 2 ) , B ( 1 , – 2 ) Equation of normal at A d y d x = 1 y - 2 = - 1 x - 1 x + y - 3 = 0 ...(i) r = Distance of line (i) from 3 , - 2 r = 3 - 2 - 3 2 = 2 r 2 = 2

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