(B) Let the coordinates of the moving point be $(x, y)$.The distance of the point $(x, y)$ from the $x$-axis is $|y|$.The distance of the point $(x, y

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(B) Let the coordinates of the moving point be $(x, y)$.The distance of the point $(x, y)$ from the $x$-axis is $|y|$.The distance of the point $(x, y)$ from the origin $(0, 0)$ is $\sqrt{x^2 + y^2}$.According to the problem,$4 \times (\text{distance from } x\text{-axis}) = (\text{distance from origin})^2$.Substituting the values,we get $4|y| = (\sqrt{x^2 + y^2})^2$.This simplifies to $4|y| = x^2 + y^2$.Rearranging the terms,we get $x^2 + y^2 - 4|y| = 0$.

Class 11 Mathematics 1 Conic Sections: Circle Locus Related Problem

Easy

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
$x^2 + y^2 - 4y = 0$
B
$x^2 + y^2 - 4|y| = 0$
C
$x^2 + y^2 - 4x = 0$
D
$x^2 + y^2 - 4|x| = 0$

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1 Conic Sections: Circle

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Locus Related Problem

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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?

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