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P3 Circle question watch

1. If you are given 3 points x, y and z, which I know its coordinates and they all pass through the circle C, what is the equation of the circle?

The coordinates are (0,2), (3,7), (2,11)
2. (Original post by BlueAngel)
If you are given 3 points x, y and z, which I know its coordinates and they all pass through the circle C, what is the equation of the circle?

The coordinates are (0,2), (3,7), (2,11)
call A (0,2)
B (3,7)
C (2,11)

find the perpendicular bisector of AB and BC (any two pairs, it doesnt matter)
the perp. bisectors cross at the centre
you can calculate the radius once you know the centre (using one of the points)
3. (Original post by BlueAngel)
If you are given 3 points x, y and z, which I know its coordinates and they all pass through the circle C, what is the equation of the circle?

The coordinates are (0,2), (3,7), (2,11)
you need to substitute them into following equation nd solve simultaneously:

x^2 + y^2 + 2fx + 2gx + c = 0

where centre of circle = (-f,-g)
4. Yeah I understand thanx.
5. (Original post by Hoofbeat)
you need to substitute them into following equation nd solve simultaneously:

x^2 + y^2 + 2fx + 2gx + c = 0

where centre of circle = (-f,-g)
But how does that prove that the equation lies on the same line?
6. (Original post by Silly Sally)
But how does that prove that the equation lies on the same line?
f, g and c will be the same in each equation, so you will end up with 3 equations, 1 for each point you are given, and each equation has 3 unknowns.

Solve simultaneously to find f and g and c
7. (Original post by JamesF)
f, g and c will be the same in each equation, so you will end up with 3 equations, 1 for each point you are given, and each equation has 3 unknowns.

Solve simultaneously to find f and g and c
But that still doesn't prove that they lie on the circle - they could be any points - couldn't they - or am i missing the point?
8. (Original post by Silly Sally)
But that still doesn't prove that they lie on the circle - they could be any points - couldn't they - or am i missing the point?
The question says that they all lie on the circle.
9. (Original post by JamesF)
The question says that they all lie on the circle.
OH sorry!!!! I can't read!! That's what else I need - the inability not to read!!!

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