Question

find the locus of a point which moves such that its distance from the origin is three times its distance from x-axis??

Answer 1

here dimensions should be given ..is it a 2D or 3D question

any comment welcome

Answer 2

The locus of the point is x² - 8y² = 0

Step-by-step explanation:

Let the point be A(x , y) as shown in the attached figure.

The distance of the point A(x,y) from the x- axis is y.

Hence, AB = y

Now, find the distance of this point from the origin using the distance formula

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\OA=\sqrt{(x-0)^2+(y-0)^2}\\\\OA=\sqrt{x^2+y^2}$

Now, it has been given that its distance from the origin is three times its distance from x-axis. Thus, we have

OA = 3 AB

Substituting the values, we get

$\sqrt{x^2+y^2}=3y$

Squaring both sides, we get

$(\sqrt{x^2+y^2})^2=(3y)^2\\\\x^2+y^2=9y^2\\\\x^2-8y^2=0$

Hence, the locus of the point is x² - 8y² = 0

#Learn More:

Find the locus of the point, the absolute value of difference of the distances of which from the points (2,2) and (0,0) is 2.identify the curve represented by the locus

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