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Question

Question: The equation to the locus of a point which moves so that its distance from x-axis is always one half...

The equation to the locus of a point which moves so that its distance from x-axis is always one half its distance from the origin is-

A

x2 + 3y2 = 0

B

x2 – 3y2 = 0

C

3x2 + y2 = 0

D

3x2 – y2 = 0

Answer

x2 – 3y2 = 0

Explanation

Solution

Let the point (h, k)

Given k = 12\frac { 1 } { 2 } h2+k2\sqrt{h^{2} + k^{2}}

squaring 4k2 = h2 + k2

Ž h2 – 3k2 = 0

\ locus x2 – 3y2 = 0