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 = 21 h2+k2
squaring 4k2 = h2 + k2
Ž h2 – 3k2 = 0
\ locus x2 – 3y2 = 0