What is the polar of the focus of a parabola?

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(C) For a parabola $y^2 = 4ax$,the focus is at $(a, 0)$.The equation of the polar of a point $(x_1, y_1)$ with respect to the parabola $y^2 = 4ax$ is

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Directrix

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(C) For a parabola $y^2 = 4ax$,the focus is at $(a, 0)$.The equation of the polar of a point $(x_1, y_1)$ with respect to the parabola $y^2 = 4ax$ is given by $yy_1 = 2a(x + x_1)$.Substituting the focus $(a, 0)$ into the equation,we get $y(0) = 2a(x + a)$,which simplifies to $0 = 2a(x + a)$.Since $a 
eq 0$,we have $x + a = 0$,or $x = -a$.This is the equation of the directrix of the parabola.Therefore,the polar of the focus is the directrix.

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