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

  (5,4)

Answer 1

The correct option is D

(5,4)

Finding which of the points does not lie on it:

Slope of tangent

$$\begin{gathered} So,m(-2)=-1 \\ \Rightarrow m=\frac{1}{2} \\ Equation\mathbf{:}\mathit{y}\mathbf{=}\mathit{m}\mathit{x}\mathbf{+}\frac{\mathbf{a}}{\mathbf{m}} \\ \Rightarrow y=\frac{1}{2}x+\frac{3}{2\times {\displaystyle \frac{1}{2}}}(a=\frac{6}{4}=\frac{3}{2}) \\ \Rightarrow y=\frac{x}{2}+3 \\ \Rightarrow 2y=x+6 \end{gathered}$$

Hence, Point (5,4) will not lie on it.