Question

Tangents are drawn from the point $(-1,2)$ on the parabola $y^2=4x$. The length, these tangents will intercept on the line $x=2$

• A. $6$
• B. $6\sqrt{2}$
• C. $2\sqrt{6}$
• D. None of these

Answer 1

The correct option is B $6\sqrt{2}$

let slope of tangent be $m$
So equation of tangent is
$y=mx+\frac{a}{m}$
Now tangent passes through $(-1,2)$ so
$\Rightarrow m^2+2m-1=0$
$\Rightarrow m=-1\pm \sqrt{2}$
equation of tangents are
$y=(-1+\sqrt{2})x+\frac{1}{-1+\sqrt{2}}$ ........ (i)
$y=(-1-\sqrt{2})x-\frac{1}{1+\sqrt{2}}$ ........ (ii)
Intercept of tangent (i) & (ii) on line $x=2$ is
$y_1=3\sqrt{2}-1and{y}_2=-3\sqrt{2}-1$ respectively
Thus length of the intercept $=y_1-y_2=6\sqrt{2}$