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 $NOT$ lie on it?

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

Answer 1

Answer: (C)

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