Question

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

• A. $(1,2)$
• B. $(1,-2)$
• C. $(4,-4)$
• D. $(4,4)$

Answer 1

Answer: (B), (D)

$(4,4)$

Given parabola : $y^2=4x$
$\Rightarrow a=1$
Equation of chord of contact from $(-2,1)$ is
$T=0\Rightarrow y\left(1\right)-2(x-2)=0\Rightarrow y-2x+4=0$

Solving this chord of contact and parabola equation will give the point of contact
$(2x-4{)}^2=4x$
$\Rightarrow 4x^2-16x+16=4x$
$\Rightarrow 4x^2-20x+16=0$
$\Rightarrow x^2-5x+4=0$
$\Rightarrow x=1,4$
From the equation of chord of contact
for $x=1\Rightarrow y=-2$
for $x=4,\Rightarrow y=4$