The equation of a tangent to the parabola y^2=8x is y=x+2.

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:

Accepted Answer

Parabola ${y^2} = 8x$

We know that the locus of point of intersection of two perpendicular tangents to a

parabola is its directrix.  Point must be on the directrix of parabola

as equation of directrix $$x + 2 = 0 \Rightarrow x =  - 2$$

Hence the point is $$\left( { - 2,0} \right)$$

Solutions · 1