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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
3 years ago

Jitender Singh
IIT Delhi
158 Points
										Ans: 90Sol: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 & RegardsJitender SinghIIT DelhiaskIITians Faculty

3 years ago
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