Question

A point point P moves so that its distance from the point (0,20) is twice its distance from B(-4,5). What is the locus of P?

Answer 1

Have you tried anything ?

Answer 2

well i tried the \[P(0,20) = 2PB \] then applied the distance formula , to get the locus and it did not give me the right answer

Answer 3

what i can tell is that it is a parabola of center (-4,5) and vertex (-4/3,25/3)
but i couldn't find the equation

Answer 4

use focal directix property.....

Answer 5

its not a equation its an locus, try using thee distance formula

Answer 6

@Rish you should get the right answer, probably some bugs

Answer 7

@FoolForMath it comes out to be close but i don't know if i have arranged it right as the question asked

Answer 8

I am sure you are making some mistake.

Answer 9

from the distance formula, all i am getting is circle. co-efficient of x^2 and y^2 are same

Answer 10

but hoblos says it's a parabola

Answer 11

find it's eccentricity....

Answer 12

its a locus which suits the points of a parabola

Answer 13

http://www.wolframalpha.com/input/?i=2*+sqrt%28+%28x%2B4%29^2+%2B+%28y-5%29^2%29+%3D+sqrt%28x^2+%2B+%28y-20%29^2%29

Answer 14

i only used the condition given in your question

Answer 15

wait ill try give it shot it should come out right

Answer 16

Just P(0,20)=2P(-4,5). Taking P as (x,y) and applying Distance formula we get the locus of (x,y) ie, the said point P as\[x ^{2}+y ^{2}+16x+20y-318=0\]
And its not a parabola as said by someone above coz both the terms x^2 and y^2 are squared and its satisfying the circle equation as the coefficients of x^2 and y^2 are same.

Answer 17

Here's my attempt at the problem