Quantitative Aptitude Ques 937

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?

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 $ (x,y) $ be the point. According to the question, $ 4\sqrt{{{(x-x)}^{2}}+y^{2}}=x^{2}+y^{2} $

$ \Rightarrow $ $ 4| y |=x^{2}+y^{2} $

$ \Rightarrow $ $ x^{2}+y^{2}-4| y |=0 $

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