Coordinate Geometry Question 131
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
[Karnataka CET 2004]
Options:
A) $ x^{2}+y^{2}-4y=0 $
B) $ x^{2}+y^{2}-4|y|=0 $
C) $ x^{2}+y^{2}-4x=0 $
D) $ x^{2}+y^{2}-4|x|=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let the required point be $ (x_1,y_1) $ . Then, according to question, $ 4|y_1|=(x_1^{2}+y_1^{2}) $
therefore $ x_1^{2}+y_1^{2}-4| y_1 |=0 $ Replace $ (x_1,y_1) $ from $ (x,y) $ , then $ x^{2}+y^{2}-4y=0 $ is the required locus.
BETA
