Simple Locus (1 Viewer)

[Buiboi]

How do you do the questions where its like a point P(x,y) is like twice as far form the line x=3 to that of line y=-2 or something liek that...

or point P(x,y) is twice as far from point A(-2,3) to that of B(4,5)

everytime i do it i never get the answer not sure if my method is wrong or its my algebra so yeah

 

[bos1234]

post an example question

 

[zooy]

Ok, taking the example u gave, A(-2,3), B(4,5). Lets have an arbitray point on the locus M(x,y). So that MA =2MB
Then using algebra (distance formula L=sqrt(x^2+y^2))
sqrt((x+2)^2+(y-3)^2)=2sqrt((x-4)^2+(y-5)^2)
then square both sides u have
(x^2+4x+4)+(y^2-6y+9)=4(x^2-8x+16+y^2-10y+25)
and then you can rearrange it, and finally u will get 3x^2-36x+3y^2-34y+151=0, which u notice is a circle.