# Math Help - Circles

1. ## Circles

Let A and B be the points of (-1,0) and (2,0) respectively and let P be the variable point (x,y).

i) write down expressions for PA and PB in terms of x and y

ii) suppose that P moves such that PA=2PB. Deduce that P moves on a circle

iii) Hence find the center and radius of this circle

2. Hello,

Originally Posted by Misa-Campo
Let A and B be the points of (-1,0) and (2,0) respectively and let P be the variable point (x,y).

i) write down expressions for PA and PB in terms of x and y
You should know the formula for a distance between 2 points :
M(a,b) N(c,d)
Then

Then for example

ii) suppose that P moves such that PA=2PB. Deduce that P moves on a circle
Square the equality PA=2PB it's far easier to work on this than the square roots that PA and PB represent.

if you can't find the solution, tell me what you've done and we'll work it out ^^

iii) Hence find the center and radius of this circle
Equation of a circle, of radius R and center O(m,n) :

3. ## Thanks

Originally Posted by Moo
Hello,

You should know the formula for a distance between 2 points :
M(a,b) N(c,d)
Then

Then for example

Square the equality PA=2PB it's far easier to work on this than the square roots that PA and PB represent.

if you can't find the solution, tell me what you've done and we'll work it out ^^

Equation of a circle, of radius R and center O(m,n) :
Thanks, im kinda get it now but still stuck on the mid question, heres what i got:

dunno what to do after that

4. That's a good start !

Divide the equation by 3 and see if you can complete squares

5. ohhhhhh i see