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Standard Equation of Ellipse

The equation ...

Question

The equation of the locus of the point which moves equidistant form the coordinate axes is:

x - y = 0

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x + y = 0

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

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

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Solution

The correct option is C $x^{2} - y^{2} = 0$
Let P(h,k) be any arbitrary point , then
(distance from y axis) $| h | = | k |$ (distance from x axis)
squaring on both sides we get,
$h^{2} = k^{2}$
$x^{2} = y^{2}$

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