Tangents at the extremities of any focal chor | vedclass

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(B) Let the parabola be $y^2 = 4ax$. The extremities of a focal chord are $P(at_1^2, 2at_1)$ and $Q(at_2^2, 2at_2)$,where $t_1t_2 = -1$.The tangents a

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On the directrix

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(B) Let the parabola be $y^2 = 4ax$. The extremities of a focal chord are $P(at_1^2, 2at_1)$ and $Q(at_2^2, 2at_2)$,where $t_1t_2 = -1$.The tangents at $P$ and $Q$ intersect at the point $(at_1t_2, a(t_1+t_2))$.Substituting $t_1t_2 = -1$,the point of intersection is $(-a, a(t_1+t_2))$.Since the directrix of the parabola $y^2 = 4ax$ is $x = -a$,the intersection point lies on the directrix.

Tangents at the extremities of any focal chord of a parabola intersect

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