Answers

2014-08-24T19:52:02+05:30
The distance of any point from x-axis is the value of ordinate.
So now if P(x, y) is a point, then it's distance from x-axis is d(say).

d =  \left \{ {{y : y \geq 0} \atop {-y:y < 0}} \right.

Also the distance of any point P(x,y) is given by square-root of sum of squares of abscissa and ordinate, So

d_o_r_i_g_i_n = \sqrt{ x^{2} + y^{2} }

Assuming y  \geq  0

\sqrt{ x^{2} + y^{2} } - y = c \\ \\ \sqrt{ x^{2} + y^{2} } = y + c \\ \\ x^{2} + y^{2} = (y + c) ^2 \\ \\ x^{2} + y^{2} = y^{2} + c^{2} + 2(c) (y) \\ \\ x^{2} - 2(c)(y) - c^{2} = 0

Thus,
Locus =  \left \{ {{ x^{2} - 2(y)(c) -  c^{2} : y  \geq 0} \atop { x^{2} + 2(c)(y) -  c^{2} : y < 0}} \right.
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