Question

find the equation ofthe locus of a point which moves in the plane so that its distance from (-2,0) is always three times its distance fromt he origin

Answer 1

thats a parabola

Answer 2

the question after it says shows that the locus is a circle...

Answer 3

the distance from its single foci is 3times its distance to the origin .... might be eliptic

Answer 4

i cant tell :)

Answer 5

hey amistre.

Answer 6

yes? :)

Answer 7

if v hav a graph of x = 1, then wht will b y ?

Answer 8

y will be lonely

Answer 9

but i cant write this LONELY thing,

Answer 10

\(\color{#f2e526}{\text{i}}\)\(\color{#3f5611}{\text{f}}\)\(\color{#b55857}{\text{ }}\)\(\color{#52da8d}{\text{x}}\)\(\color{#43eb8c}{\text{=}}\)\(\color{#6ed573}{\text{1}}\)\(\color{#2fcdae}{\text{;}}\)\(\color{#2dadc9}{\text{ }}\)\(\color{#a2bf6f}{\text{y}}\)\(\color{#3bddb5}{\text{ }}\)\(\color{#fb28fd}{\text{w}}\)\(\color{#35b173}{\text{i}}\)\(\color{#da931a}{\text{l}}\)\(\color{#e1c579}{\text{l}}\)\(\color{#d2396b}{\text{ }}\)\(\color{#5398c5}{\text{a}}\)\(\color{#eefeac}{\text{l}}\)\(\color{#3adb86}{\text{w}}\)\(\color{#aabcb4}{\text{a}}\)\(\color{#d9ac7d}{\text{y}}\)\(\color{#bd46ed}{\text{s}}\)\(\color{#fc8c8d}{\text{ }}\)\(\color{#1c55a2}{\text{b}}\)\(\color{#ffa143}{\text{e}}\)\(\color{#1de66e}{\text{ }}\)\(\color{#bbf359}{\text{l}}\)\(\color{#d5f6ff}{\text{o}}\)\(\color{#cedad1}{\text{n}}\)\(\color{#4c94be}{\text{e}}\)\(\color{#f7ad29}{\text{l}}\)\(\color{#49a7f2}{\text{y}}\)\(\color{#864fb7}{\text{}}\)

Answer 11

lol okay...

Answer 12

y not exist on a vertical line do it?

Answer 13

no.

Answer 14

umm so...circle...or no...where'd amistre go?

Answer 15

but wht should i write?

Answer 16

location of a point which moves in the plane

its distance from (-2,0) is always 3x distance from (0,0)

Answer 17

yes...

Answer 18

what is its distance if it IS the origin

Answer 19

[\sqrt{(x-0)^2+(y-0)^2}]

Answer 20

for my final answer i got 2x^2-4x-4

Answer 21

the point (-3,0) is on this path; and so is (-1.5 , 0 )

Answer 22

right?

Answer 23

right!

Answer 24

and we did that because thats our new second point?

Answer 25

thats just one point that is 3 times the distance to the origin as it is to the -2,0

Answer 26

i just tried to figure it for a point above and below the point; but my angle comes back as 0 or 180

Answer 27

this question is very interesting...

Answer 28

its cause I tried to force it to be 3 and 1 lol instead of a ration

Answer 29

if i did it right; we get points above and below it at a distance of 1/sqrt(2)

Answer 30

well the good news is it aint a circle

Answer 31

thats bad news lol...

Answer 32

lets flip it over to the positive side

from 0 to 2 is our origin and point;

3,0 is 1 away from 2 and 3 away fromm 0; its good

1.5 is 3/2 from 0 and 1/2 from 2

so we have 2 points (1.5,0) and (3,0) that satisfy our misinterpretations

Answer 33

u are over complicating it

Answer 34

the center of these 2 points is of course 2.25; if this was a circle then the point that is above and below it would match our problem

Answer 35

overcomplicating is what I do when im using what i know to get to where i dont know

Answer 36

\[\sqrt{(x+2)^2 +y^2} = 3 \sqrt{ x^2+y^2}\]

Answer 37

square both sides expand, group and complete the squares

Answer 38

.75 would be our radius by my conjecture; so the point (2.25, .75) would have to pythag to = 9

Answer 39

(x^2 +4x +4 +y^2 = 9 ( x^2 +y^2)

Answer 40

well, not 9; but 3(.75 ) to be good

Answer 41

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

Answer 42

divide through by 4

Answer 43

no 8

Answer 44

x^2 -(1/2)x +y^2 = (1/2)

Answer 45

(x-(1/4) )^2 +y^2 = (1/2) + (1/16)

Answer 46

(x-(1/4))^2 +y^2 = 9/16

Answer 47

i got the same thing but i forgot tot square my 3

Answer 48

circle ecentre ( (1/4) , 0 ) radius 3/4

Answer 49

if hes right; id go with it cause I cant get nothing beating my head against the wall lol

Answer 50

lol aww thanks so much amistre...

Answer 51

so elece you used method of completing of the squares to find the centre and radius

Answer 52

THANKS SO MUCH ELECENGINEER!!! and AMISTRE!!!

Answer 53

9/16 is not 3/4

Answer 54

circle is x^2 +y^2 = r^2

Answer 55

sqrt(9/16)= 3/4