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  4. A tangent is drawn to the parabola y2=6 x which is perpendicular to the line 2 x + y =1 Which of the following points does NOT lie on it?

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Q. A tangent is drawn to the parabola $y^{2}=6 x$ which is perpendicular to the line $2 x + y =1$ Which of the following points does $NOT$ lie on it?

JEE MainJEE Main 2021Conic Sections

Solution:

Slope of tangent $= m _{ T }= m$
So, $m (-2)=-1$
$ \Rightarrow m =\frac{1}{2}$
Equation : $y = mx +\frac{ a }{ m }$
$\Rightarrow y=\frac{1}{2} x+\frac{3}{2 \times \frac{1}{2}}\left(a=\frac{6}{4}=\frac{3}{2}\right)$
$\Rightarrow y=\frac{x}{2}+3$
$\Rightarrow 2 y=x+6$
Point (5,4) will not lie on it