The equation of the locus of a point whose di | vedclass

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Question

(D) Let the point be $P(x, y, z)$.The distance of point $P(x, y, z)$ from the $XY$-plane is given by $|z|$.The distance of point $P(x, y, z)$ from the

Vedclass · Accepted Answer

$4x^2 + 4y^2 - z^2 = 0$

Vedclass · Answer

(D) Let the point be $P(x, y, z)$.The distance of point $P(x, y, z)$ from the $XY$-plane is given by $|z|$.The distance of point $P(x, y, z)$ from the $Z$-axis is given by $\sqrt{x^2 + y^2}$.According to the problem,the distance from the $XY$-plane is twice the distance from the $Z$-axis:$|z| = 2 \sqrt{x^2 + y^2}$.Squaring both sides,we get:$z^2 = 4(x^2 + y^2)$.$z^2 = 4x^2 + 4y^2$.Rearranging the terms,we get:$4x^2 + 4y^2 - z^2 = 0$.Thus,the correct option is $D$.

The equation of the locus of a point whose distance from the $XY$-plane is twice its distance from the $Z$-axis is:

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