points (1,2),(3,-4),(5,-6) laying on the circumference of a circle,find the cordinate of centre?:confused:

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- Nov 23rd 2006, 01:47 AManjanaco-ordinate geometry
points (1,2),(3,-4),(5,-6) laying on the circumference of a circle,find the cordinate of centre?:confused:

- Nov 23rd 2006, 02:09 AMearboth
Hello, Anjana,

I assume that the equation of a circle in with the centre is:

Now plug in the values yxou know. You'll get 3 equations:

Expand the LHS of these equations. Then substract equ2 from equ1 and equ3 from equ1. You'll get 2 linear equations without any squares which will give you the values of m1 and m2. Afterwards you can calculate the value of r.

For confirmation only M(11, 2) and r = 10

EB - Nov 23rd 2006, 08:08 AMSoroban
Hello, anjana!

EB has the best solution.

Here's another approach . . . requiring more Thinking.

Quote:

Points are on the circumference of a circle.

Find the coordinates of the centre.

The circumcenter is the intersection of the perpendicular bisectors of the sides.

The midpoint of is . The slope of is:

The equation of the perpendicular bisector of is:

. .

The midpoint of is The slope of is

The equation of the perpendicular bisector of is:

. .

The perpendicular bisectors intersect when:

. .

Then: .

Therefore, the center of the circle is: .