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 the x axis is ?
A) ${x^2} - 8{y^2} = 0$
B) $4{x^2} - {y^2} = 0$
C) ${x^2} - 8{y^2} = 0$
D) ${x^2} - 8{y^2} = 0$

Answer 1

Hint: To determine the locus of a point we need to assume P( x,y ) be a point whose locus needs to be found. Calculating the distance from x axis and the origin , we substitute and equate the values to get the desired answer.

Complete step-by-step answer:
Let P( x,y ) be the point whose locus needs to be found .
The distance of P( x,y ) from the origin (0,0) = $\sqrt {{{\left( {x - 0} \right)}^2} + {{\left( {y - 0} \right)}^2}} = \sqrt {{x^2} + {y^2}} $ ( Using distance formula )
Now the distance of P( x,y ) from x axis = y
According to the question,
$\sqrt {{x^2} + {y^2}} = 3 \times y$
$ \Rightarrow {x^2} + {y^2} = 9{y^2}$
$ \Rightarrow {x^2} - 8{y^2} = 0$

Note: In such questions remember that the distance of any point ( x,y ) from x axis and y axis would be y and x respectively . Always remember to recall the distance formula to get to the required result .