The equation of the locus of a point whose di | vedclass

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(B) Let the point be $P(h, k)$.Given that the distance of $P$ from $(a, 0)$ is equal to its distance from the $y$-axis.The distance of $P(h, k)$ from

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

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(B) Let the point be $P(h, k)$.Given that the distance of $P$ from $(a, 0)$ is equal to its distance from the $y$-axis.The distance of $P(h, k)$ from $(a, 0)$ is $\sqrt{(h-a)^2 + (k-0)^2}$.The distance of $P(h, k)$ from the $y$-axis is $|h|$.Equating the distances: $\sqrt{(h-a)^2 + k^2} = |h|$.Squaring both sides: $(h-a)^2 + k^2 = h^2$.$h^2 - 2ah + a^2 + k^2 = h^2$.$k^2 - 2ah + a^2 = 0$.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 whose distance from $(a, 0)$ is equal to its distance from the $y$-axis is

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