Question

Hello brainiacs

find the equation of locus of a point P for which distance from P to (0,5) is double the distance from P to y axis.....?
​

Answer 1

Answer:

please refer to the attachment

I hope it would help you

thank you.

if it's right, leave a like,

u may report, when answer is wrong

thank you

Answer 2

Concept: A locus (plural: loci) is a set of all points (often, a line, a line segment, a curve, or a surface) whose position fulfils or is determined by one or more defined conditions in geometry.

Given: A point (0,5)

           distance from P to (0,5) is double the distance from P to y-axis, i.e., $2d_{y} = PA$

To find: The equation of locus of a point P

Solution:

Let P(x,y) be any point in X-Y plane

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

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

Distance of P from y- axis

$d_{y} = | x|$

$2d_{y} = PA\\2 |x| = \sqrt{x^{2} + (y-5)^{2}}\\4x^{2} = {x^{2} + (y-5)^{2}$

$3x^{2} - (y-5)^{2} = 0\\3x^{2} - (y^{2} + 25 - 10y) = 0\\3x^{2} - y^{2} - 25 + 10y = 0$

Hence the required  equation is $3x^{2} - y^{2} - 25 + 10y = 0$

#SPJ2