Circles

[aznboy50]

Hey guys,

How do I find the equation of a circle when I know 3 points that are on the circle?

How do I find where two circles intercept if I have their respective equations?

Thank you

[TrueTears]

(x-h)^2+(y-k)^2=r^2

3 unknowns h,k,r

make 3 equations and solve

[aznboy50]

Shit, thanks TT, I was doing that previously but for some stupid reason was subbing x-ordiante for h and y-ordinate for k. Then, not realising why I couldn't find h and k... Possibly the dumbest mistake ever made.

How do I find the intercept where two circles intercept?

[Andiio]

Make both equations equal each other then solve.

[aznboy50]

Make both equations equal each other then solve.

I did think of that >.<

But you will be left with an x-variable and a y-variable in the equation?

[aznboy50]

Hrmm...

Could I maybe solve for y.

Then sub the y-value in one of the original equations in terms of x. Then solve for x?

Is this possible?

[vea]

It is just the same as any usual simultaneous equation but having the x and y both on one side at the start may throw people off. :S

[brightsky]

Yeah for example, if you're given the points (1, 3), (-3,-8) and (-4, 3). You're general circle equation is (x-h)^2 +(y-k)^2 = r^2.

Sub the points in:

(1 - h)^2 + (3 - k)^2 = r^2...(1)
(-3 - h)^2 + (-8-k)^2 = r^2...(2)
(-4 - h)^2 + (3 -k)^2 = r^2...(3)

(2) - (1):
8h + 22k + 63 = 0...(4) [Do note this is after simplification]

(3) - (2):
2h -22k - 48 = 0...(5) [So is this]

Do (4) + (5) and then solve for h. Plug h back into (4) or (5) to find k. And then plug those values back into (1), (2) or (3) to find r.