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

Answer: (B)

Let slope of tangent be $m$ So equation of tangent is
$y=mx+\frac{1}{m}$
Now tangent passes through $(−1,2)$ so
$⇒m^2+2m−1=0$
$⇒m=−1Â\pm \sqrt{2}$
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
$y_1=3\sqrt{2}−1$ & $y_2=−3\sqrt{2}−1$ respectively.
Now $y_1−y_2$ is $6\sqrt{2}$