p3 circles Watch

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topdude
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#1
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how do u work out the equation of a circle, by knowing 3 points that go through it? The points are (2,0) (8,0) and (5,9)
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Bill.L
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suppose the eq is x^2+y^2+ex+fy+c=0, substituting all poins into it, solve e,f,c
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El Stevo
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those points are an isosceles triangle...

edit: got it!

work out the angle at the top of it, double it. you then have two points, two radii, angle at the centre and the distance between the two points, so you cna work out the radius, with which you can work out the equation... i'll rig a diagram up in paint to show you if you don't understand this...
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topdude
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(Original post by Bill.L)
suppose the eq is x^2+y^2+ex+fx+c=0, substituting all poins into it, solve e,f,c
id love 2 say that i can work with that, but i end up gettin it wrong
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john !!
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or you can form a triangle from the three points, find the perpendicular bisector of two of the edges and solve where they meet to find the centre. the radius will be the distance from this point to any of the vertices.

this method only uses coordinate geometry and is incredibly boring. do the above method if you can solve 3 simultaneous equations (and can complete the square). only remember that f should be the coefficient of y, not x.
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Bill.L
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sorry i just typed wrong, but i have changed
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topdude
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#7
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(Original post by El Stevo)
those points are an isosceles triangle...

edit: got it!

work out the angle at the top of it, double it. you then have two points, two radii, angle at the centre and the distance between the two points, so you cna work out the radius, with which you can work out the equation... i'll rig a diagram up in paint to show you if you don't understand this...
i didnt even read ur 1 till just now......yea i get it now....thank u
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lgs98jonee
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(Original post by topdude)
how do u work out the equation of a circle, by knowing 3 points that go through it? The points are (2,0) (8,0) and (5,9)
for 1 point, you could notice that (2,0) and (8,0) are directly across from one another. this means that the x coordiante of the centre is going to be 5. this is due to the circle's symmetry.

equation of circle in (x-a)^2+(y-b)^2=r^2
where a,b is circle's centre and r=radius. anyway, notice the fact that two points have the same x or y coordinate can help you to find circle's centre more easily. :creep:
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