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(A) Let the moving point be $P(h, k)$.The distance of $P(h, k)$ from the point $(a, 0)$ is $\sqrt{(h - a)^2 + (k - 0)^2}$.The distance of $P(h, k)$ fr

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$y^2 - 2ax + a^2 = 0$

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(A) Let the moving point be $P(h, k)$.The distance of $P(h, k)$ from the point $(a, 0)$ is $\sqrt{(h - a)^2 + (k - 0)^2}$.The distance of $P(h, k)$ from the $y$-axis (the line $x = 0$) is $|h|$.According to the problem,these distances are equal:$\sqrt{(h - a)^2 + k^2} = |h|$Squaring both sides,we get:$(h - a)^2 + k^2 = h^2$$h^2 - 2ah + a^2 + k^2 = h^2$$-2ah + a^2 + k^2 = 0$Replacing $(h, k)$ with $(x, y)$,the equation of the locus is:$y^2 - 2ax + a^2 = 0$.

The equation of the locus of a point which moves so as to be at equal distances from the point $(a, 0)$ and the $y$-axis is

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