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If the normals 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 4 is equal to

Correct answer

4

Step-by-step solution

End points of the latus rectum of the parabola y 2 = 4 x and 1 , ± 2 . Equation of the normals at points 1 , ± 2 are y = - x + 3 and y = x - 3 rr x + y - 3 = 0 and x - y - 3 = 0 These lines are tangent to the circle x - 3 2 + y + 2 2 = r 2 ∴ 3 ± 2 - 3 1 + 1 = r = 2 Hence, r 4 = 4

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