(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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(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:$y^2 - 2ax + a^2 = 0$.

Class 11 Mathematics 10-1.Circle and System of Circles Locus Related Problem

Easy

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

A
$y^2 - 2ax + a^2 = 0$
B
$y^2 + 2ax + a^2 = 0$
C
$x^2 - 2ay + a^2 = 0$
D
$x^2 + 2ay + a^2 = 0$

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10-1.Circle and System of Circles

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Locus Related Problem

$A$ circle of constant radius $a$ passes through the origin $O$ and cuts the coordinate axes at points $P$ and $Q$. The equation of the locus of the foot of the perpendicular from $O$ to $PQ$ is:

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The locus of the point of intersection of the tangents to the circle $x^2+y^2=16$,such that the angle between them is $60^{\circ}$,is

MediumMHT CET 2025

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If $\frac{x}{\alpha} + \frac{y}{\beta} = 1$ touches the circle $x^2 + y^2 = a^2$,then the point $(\frac{1}{\alpha}, \frac{1}{\beta})$ lies on a/an

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$A$ rod of length $12 \, cm$ moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point $P$ on the rod,which is $3 \, cm$ from the end in contact with the $x-$axis.

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Consider a rigid square $ABCD$ as in the figure with $A$ and $B$ on the $X$ and $Y$-axes,respectively. When $A$ and $B$ slide along their respective axes,the locus of $C$ forms a part of

KVPY 2017

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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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