The equations of the tangents to the parabola | vedclass

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(D) The ends of the latus rectum of the parabola $y^2 = 4ax$ are $(a, 2a)$ and $(a, -2a)$.The equation of the tangent to the parabola $y^2 = 4ax$ at p

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Both $(A)$ and $(B)$

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(D) The ends of the latus rectum of the parabola $y^2 = 4ax$ are $(a, 2a)$ and $(a, -2a)$.The equation of the tangent to the parabola $y^2 = 4ax$ at point $(x_1, y_1)$ is given by $yy_1 = 2a(x + x_1)$.For the point $(a, 2a)$:$y(2a) = 2a(x + a)$$y = x + a$$x - y + a = 0$For the point $(a, -2a)$:$y(-2a) = 2a(x + a)$$-y = x + a$$x + y + a = 0$Thus,the equations of the tangents are $x - y + a = 0$ and $x + y + a = 0$.

The equations of the tangents to the parabola $y^2 = 4ax$ at the ends of its latus rectum are-

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