Question

If the tangents drawn from the point $(0,2)$ to the parabola $y^2=4ax$ are inclined at an angle of $\frac{3\pi }{4}$ with axis of the parabola then the value of $a$ is:

• A. $2$
• B. $-2$
• C. $1$
• D. none of these

Answer 1

The correct option is B $-2$

Equation of tangent in slope form is $y=mx+\frac{a}{m}$
where, $m=\tan \frac{3\pi }{4}=-1$
Since, it passes through $(0,2)$
Therefore, $2=\frac{a}{-1}$
$\Rightarrow a=-2$
Ans: B