Question

What is the equation of the locus of a point which moves such that 4 times its distance from the x axis is the square of its distance from the origin.

• A. x² + y² – 4y = 0
• B. x² + y² – 4x = 0
• C. x² + y² – 4|y| = 0
• D. x² + y² – 4 |x| = 0

Answer 1

Answer: (C)

x² + y² – 4|y| = 0

Answer 2

Let coordinate of point is (h₁k)

\ according to Q.

$4\sqrt{(h - h)^{2} + k^{2}} = h^{2} + k^{2}$

Ž 4 |k| = h² + k²

\ locus of the point is

4 |y| = x² + y²

Ž x² + y² – 4 |y| = 0