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

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

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 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
askIITians Faculty

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