Question

The equation to the locus of a point P for which the distance from P to (0,5) is double the distance from P to y–axis is

Answer 1

Answer:

the answer is 4,-6

Explanation:

it is the answer of questions

Answer 2

Answer:

  The equation: $3x^2-y^2+ 10y-25=0$

Explanation:

Let P(x,y) be an arbitrary point in X−Y plane.

Therefore,the distance of P from A (0,5) is

$PA = \sqrt {x^2 + (y-5)^2$  ...........................................(i)

and the distance of P from y-axis.

  $d_y = |x|$

It is given that,

             $2 d_y = PA$

     → $2|x| = \sqrt {x^2 + (y-5)^2$

Squaring both sides of above equation,we get

            $4 x^2 = {x^2 + (y-5)^2$

       or, $3x^2 -(y-5)^2 = 0$

        $or, 3x^2-y^2+ 10y-25=0$  

    ∴The equation: $3x^2-y^2+ 10y-25=0$