A tangent is drawn to the parabola
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?

1. (1) $(0,3)$

2. (2) $(-6,0)$

3. (3) $(4,5)$

4. (4) $(5,4)$

Correct Option: , 4

Solution:

Equation of tangent $: y=m x+\frac{3}{2 m} \mathrm{~m}_{\mathrm{T}}=\frac{1}{2}(\because$ perpendicular to line $2 x+y=1$ )

: $\quad$ tangent is : $y=\frac{x}{2}+3 \quad \Rightarrow x-2 y+6=0$