Line y=2x−b cuts the parabola y=x2−4x at points A and B . The value of b for which the ∠AOB is a right angle is

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answer is 7.

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Detailed Solution

Line y=2x−b⇒ 1=2x−yb Homogenizing parabola with line x2−4x2x−yb−y2x−yb=0 Since ∠AOB=90∘∴ coefficient of x2+ coefficient of y2=0⇒ 1−8b+1b=0⇒ b=7

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