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. (- 1, 1)
• B. (0, 2)
• C. (2, 4)
• D. (-2, 0).

Answer 1

Answer: (D)

$y=mx+\frac{a}{m}$ is a tangent for all values of m where $a=2$.
For $m=1,y=x+2$
$\therefore$ the equation of the tangent $\perp$ to the given tangent is $y=-x-2$.
The reqd. point is the point of intersection of these tangents i.e., $\left(-2,0\right)$
[ $\because$ perpendicular tangents to a parabola meet on the directrix $x+2=0$]