The point of intersection of tangents at the | vedclass

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(B) The equation of the tangent at $(x_1, y_1)$ on the parabola $y^2 = 4ax$ is $yy_1 = 2a(x + x_1)$.For the parabola $y^2 = 4x$,we have $a = 1$.The co

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$(-1, 0)$

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(B) The equation of the tangent at $(x_1, y_1)$ on the parabola $y^2 = 4ax$ is $yy_1 = 2a(x + x_1)$.For the parabola $y^2 = 4x$,we have $a = 1$.The coordinates of the ends of the latus rectum are $L(1, 2)$ and $L'(1, -2)$.For point $L(1, 2)$,the tangent equation is $2y = 2(x + 1)$,which simplifies to $y = x + 1$.For point $L'(1, -2)$,the tangent equation is $-2y = 2(x + 1)$,which simplifies to $y = -(x + 1)$.Solving these two equations: $x + 1 = -(x + 1) \implies 2(x + 1) = 0 \implies x = -1$.Substituting $x = -1$ into $y = x + 1$,we get $y = 0$.Thus,the point of intersection is $(-1, 0)$.

The point of intersection of tangents at the ends of the latus-rectum of the parabola $y^2 = 4x$ is

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