A pair of tangents are drawn from a point on the directrix to a parabola y2=4ax. The angle formed by the tangents will always be 90∘
Let's draw a parabola first
p is the point on the directrix and A and B are the points where tangents from P touches the parabola.
Let P≡(−a,y), both tangents at A point is,
The equation for tangent at A point is,
for tangent at A
for tangent at B
We know slope of a tangent at a point given by parameter is (1t)
If 2 tangent are perpendicular then product of slope will be -1.
∴ Tangent are at right angle to each other