Question

The equation of a tangent to the parabola $y^2=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

• A. $(–2,0)$
• B. $(2,4)$
• C. $(0,2)$
• D. $(–1,1)$

Answer 1

The correct option is A

$(–2,0)$

The two tangents are perpendicular.

We know that perpendicular tangents to a parabola intersect at the directrix.

So, the directrix of the parabola $y^2=8x$ is $x=-2$

Putting $x=-2$ in the line $y=x+2$, we get $y=0$

Hence, The point on the line $y=x+2$ from which the other tangent to the parabola is perpendicular to the given tangent is $(-2,0)$