Thread: 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

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) :

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

That's a good start !

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

ohhhhhh i see