Question

The locus of a point,which moves in such a way that its distance from the origin (0,0) is thrice the distance from X-axis is?

Answer 1

x^2=8y.^2.....is the locus of the point

Answer 2

The thrice distance from x axis is x² - 8y² = 0

Distance from the origin = (0,0) (Given)

Let P(x,y) be a point whose locus needs to be found.

Distance of P(x,y) from x−axis= y

Distance of P(x,y) from (0,0) = √ ( x - 0)² + ( y - 0)²

= √ x² + y²

According to the question -

= √ x² + y² = 3y

= x² + y² = 9y²

= x² - 8y² = 0