points (1,2),(3,-4),(5,-6) laying on the circumference of a circle,find the cordinate of centre?
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
Hello, anjana!
EB has the best solution.
Here's another approach . . . requiring more Thinking.
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: .