Question

The equation of a tangent to the parabola y² = 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

Answer 1

The two tangents are perpendicular.

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

So, the directrix of the parabola y² = 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).