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