What are the equations of the tangents at the | vedclass

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(D) The parabola is given by $y^2 = 4ax$. The endpoints of the latus rectum are $(a, 2a)$ and $(a, -2a)$.For a point $(x_1, y_1)$ on the parabola $y^2

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Both $A$ and $B$

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

What are the equations of the tangents at the endpoints of the latus rectum of the parabola $y^2 = 4ax$?

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