Let the radius of the circle touching the parabola y 2 = x at 1,1 and having the directrix of y 2 = x as its normal is equal to k 5 units, then k is equal to

Question

Let the radius of the circle touching the parabola y 2 = x at 1,1 and having the directrix of y 2 = x as its normal is equal to k 5 units, then k is equal to,

MARKS App · Accepted Answer

Equation of normal at P is y - 1 = - 2 x - 1 y + 2 x = 3 at x = - 1 4 , y = 3 + 1 2 = 7 2 ⇒ radius = 1 + 1 4 2 + 1 - 7 2 2 = 5 5 4 ⇒ 5 5 4 = k 5 ⇒ k = 5 4 = 1.25

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