JEE MainMathematicsModerateParabola

A line y = 2x - b cuts the parabola y = x^2 - 4x at points A
and B such that the value of b for which $\angle$ AOB is right angle is K
then value of $\frac{11K}{5}$ is

Show answer and solution

The line is y = 2x - b, i.e., 1=

\frac{2x - y}{b}

Homogenizing parabola with line, we get

x^{2} - 4x\left( \frac{2x - y}{b} \right) - y\left( \frac{2x - y}{b} \right) = 0

Since

\angle

AOB = 90º
Coefficient of x^2 + coefficient of y^2 = 0
or 1

- \frac{8}{b} + \frac{1}{b} = 0

or b = 7 = k
so,

\frac{11k}{5}

=15.4

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx

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