Question

If a tangent is drawn to the parabola $y^2=4x$ through $(-2,1)$, then the point of contact can be:

• A. $(2,1)$
• B. $(1,2)$
• C. $(1,-2)$
• D. $(2,\sqrt{2})$

Answer 1

Answer: (C)

$(1,-2)$

The equation of tangent to the parabola $y^2=4x$ is $x-yt+t^2$

Since, it passes through $(-2,1)$

Therefore, $-2-t+t^2=0$

$\Rightarrow t=-1$ or $t=2$

Therefore, one point of contact is $(t^2,2t)=(1,-2)$