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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Solution

The correct option is A

$A c c o r d i n g l y, (h - a)^{2} + k^{2} = h^{2} \Rightarrow - 2 a h + a^{2} + k^{2} = 0$

Replace (h, k) by (x, y), then $y^{2} - 2 a x + a^{2} = 0$ is the required locus.

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Similar questions

List I	List II
A) An equation of the circle touching the x- axis is	1) $x^{2} + y^{2} + 2 a x + 2 a y + a^{2} = 0$
B) An equation of the circle touching the y- axis is	2) $x^{2} + y^{2} - 2 a x + 2 b y + b^{2} = 0 y$
C) An equation of the circle touching both the axes is	3) $x^{2} + y^{2} + 2 a x - 2 a y + a^{2} = 0$
D) An equation of the circle passing through (a, b) is	4) $x^{2} + y^{2} + a x - b y - 2 a^{2} = 0$

x^{2} + y^{2} - 2 a x - 2 a y + a^{2} = 0

a^{2} - 2 a (x + y) + 2 x y = 0

ABCD is a square, the length of whose side is a. Taking AB and AD as the coordinate axes, the equation of the

circle passing through the vertices of the square, is

y^{2} = 4 a x

45^{\circ}

A

x^{2} + y^{2} - 2 a x - 2 a y + a^{2} = 0

a > 0

(38, - 37)

a^{2} - 2 a

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