Question

Find the equation to the locus of the point which is equidistant from the coordinate axes.
[Ans:
$x ^{2} - {y}^{2} = 0$
]
Need the Explanation to this question..​

Answer 1

Answer:

Let P(h,k) be any point in the locus.

Let PM be the perpendicular distance of P fro x-axis, i.e.,

PM=∣x∣

Let PNeft be the perpendicular distance of P fro y-axis, i.e.,

PN=∣y∣

∵PM=PN(Given)

⇒∣x∣=∣y∣

Squaring both sides, we have

x

2

=y

2

⇒x

2

−y

2

=0.

Thus, locus of P is x

2

−y

2

=0.