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

The correct option is D $(-2,0)$

Given that, equation of tangent to the parabola $y^2=8x$ is $y=x+2$.
Equation of the line which is perpendicular to the given tangent is $y=-x+c$
But, $y=-x+c$ is also tangent to the parabola.
$\Rightarrow c=\frac{a}{m}=-2$
i.e Equation of tangent perpendicular to $y=x+2$ is $y=-x-2$
solving above two lines gives $(-2,0)$
$\therefore$ Required point is $(-2,0)$
Hence, option D.