The equation to the locus of a point which mo | vedclass

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Question

(B) Let the moving point be $P(x, y)$.The distance of point $P(x, y)$ from the $x$-axis is $|y|$.The distance of point $P(x, y)$ from the origin $(0,

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$x^2 - 3y^2 = 0$

Vedclass · Answer

(B) Let the moving point be $P(x, y)$.The distance of point $P(x, y)$ from the $x$-axis is $|y|$.The distance of point $P(x, y)$ from the origin $(0, 0)$ is $\sqrt{x^2 + y^2}$.According to the given condition,the distance from the $x$-axis is one-half of its distance from the origin:$|y| = \frac{1}{2} \sqrt{x^2 + y^2}$Squaring both sides,we get:$y^2 = \frac{1}{4} (x^2 + y^2)$$4y^2 = x^2 + y^2$$x^2 + y^2 - 4y^2 = 0$$x^2 - 3y^2 = 0$Thus,the required equation of the locus is $x^2 - 3y^2 = 0$.

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

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