Tangents drawn at the ends of any focal chord | vedclass

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(D) Let the ends of the focal chord be $P(at_1^2, 2at_1)$ and $Q(at_2^2, 2at_2)$.Since $PQ$ is a focal chord,$t_1 t_2 = -1$.The intersection point of

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$x + a = 0$

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(D) Let the ends of the focal chord be $P(at_1^2, 2at_1)$ and $Q(at_2^2, 2at_2)$.Since $PQ$ is a focal chord,$t_1 t_2 = -1$.The intersection point of the tangents at $P$ and $Q$ is $(at_1 t_2, a(t_1 + t_2))$.Substituting $t_1 t_2 = -1$,the $x$-coordinate becomes $x = a(-1) = -a$.Thus,the tangents intersect on the line $x = -a$,which is the directrix of the parabola.Therefore,the equation is $x + a = 0$.

Tangents drawn at the ends of any focal chord of a parabola $y^2 = 4ax$ intersect on the line

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