Q162 / 270 · NDA 2013 (Phase 2) · Mathematics

The equation of the locus of a point which is equidistant from the axes is

  • A
    y = 2x
  • B
    x = 2y
  • Correct answer
    C
    $y= \pm x$
  • D
    $2 y+x=0$

Solution

As the required line is equidistant from the axes, so its has equal inclination with two axes. Slope of such line $(m)= \pm \tan \left(45^{\circ}\right)= \pm 1$. Equation of such line will passes through origin. Hence, locus of a point equidistant from two axes will be $\begin{aligned} y-0 & = \pm 1(x-0) \\ y & = \pm x \end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions