Question

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

• A. $(0,3)$
• B. $(-6,0)$
• C. $(4,5)$
• D. $(5,4)$

Answer 1

The correct option is D $(5,4)$

For $y^2=6x,a=\frac{3}{2}$
equation of tangent $:y=mx+c$
$\Rightarrow y=mx+\frac{3}{2m}$
$\because c=\frac{a}{m}$
and
$m=\frac{1}{2}(\because$ perpendicular to line $2x+y=1)$
$\therefore$ tangent is : $y=\frac{x}{2}+\frac{3}{1}\Rightarrow x–2y+6=0$