Question

the distance of a moving point from the line x=3 is twice its distance from (-1,-2). FInd the equation of its locus.

Answer 1

let P=(x,y)
d1^2 -> use distance formula (x-3=0,(x,y))=|x-3|/sqrt(1)=(x-3)^2
d2^2 -> use distance formula between two points
d1^2 = 4*d2^2

Answer 2

can you please give an illustration?

Answer 3

and i really don't get it... -_- i'm sorry.. can you please elaborate

Answer 4

d1 is distance of (x,y) from the line x=3
d2 is distance between (x,y) and (-1,-2)

Answer 5

how will i find for the equation of the locus?

Answer 6

find d1, d2
it is given that d1=2*d2
you'd get an equation in terms of x and y

do you know what a locus is?

Answer 7

it is a set of points

Answer 8

yes but satisfying certain conditions.

Answer 9

yes.. ok.. i'll try solving that

Answer 10

so, all possible (x,y) that satisfy one or many equations.
that equation is what the question is asking you to find,

Answer 11

d1^2 -> use distance formula (x-3=0,(x,y))=|x-3|/sqrt(1)=(x-3)^2
how did you do this?

Answer 12

distance of a point from a line
\[
l\implies ax+by+c=0\quad (x_0,y_0)\\
d_1=\frac{|ax_0+by_0+c|}{\sqrt{a^2-b^2}}
\]

Answer 13

ok ok.. got it.. but do i really have to square both d to find the locus?

Answer 14

makes life easy.. d2 is a square-root remember?

Answer 15

what i got was 3x^2 + 14x + 4y^2 + 16y + 25 = 0..
is this correct?

Answer 16

3x^2 + 14x + 4y^2 + 16y + 7 = 0..

Answer 17

hope so. ;)

Answer 18

unless you did some mistake with the numbers.

Answer 19

hahaha.. ok .. i'll write what i did so you can see which part i made the mistake..

Answer 20

it's so hard to write it down.. :(

Answer 21

i know.. but its cool. should look something like that
in fact, it is a circle.

Answer 22

or an ellipse?.. the co-efficients of x^2 and y^2 are different.. so, an ellipse

Answer 23

3x^2 - 2x + 4y^2 + 8y - 3 = 0.. that's what i got.. is it correct?

Answer 24

3x^2 + 2x + 4y^2 + 8y - 3 = 0

Answer 25

yes.
you can check. put some x, like "2", find y
check distances

Answer 26

thank you so much! :))