# he angle between the tangents to the parabola y^2=4ax at the points whrer ti intersects the line x-y=a

Jitender Singh IIT Delhi
8 years ago
Ans: 90
Sol:
Let P(t1, 2at1) & Q(t2, 2at2) be the points on the parabola where line intersects the parabola. Then slope of tangents at P & Q would be:
$\frac{1}{t_{1}}, \frac{1}{t_{2}}$
Angle between tangents:
$\frac{|t_{2}-t_{1}|}{1+t_{1}t_{2}}$
Since both points lie on the line, we have
$t_{1}^{2}-2t_{1}-1=0$
$t_{2}^{2}-2t_{2}-1=0$
t1, t2are the roots of the equation
$t^{2}-2t-1=0$
Product of the roots is -1,
$t_{1}t_{2}=-1$
Angle is 90.
Thanks & Regards
Jitender Singh
IIT Delhi