How to solve the questions of coordinate geometry . Please help me to solve the coordinate geometry question easily and giving the best solution .Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).
Share
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Let A = (6, -6), B = (3, -7), C = (3, 3) are the points on a circle.
If O is the centre, then OA = OB = OC (radii are equal)
If O = (x, y) then
OA = √[(x – 6)2 + (y + 6)2]
OB = √[(x – 3)2 + (y + 7)2]
OC = √[(x – 3)2 + (y – 3)2]
Choose: OA = OB, we have
After simplifying above, we get -6x = 2y – 14 ….(1)
Similarly: OB = OC
(x – 3)2 + (y + 7)2 = (x – 3)2 + (y – 3)2
(y + 7)2 = (y – 3)2
y2 + 14y + 49 = y2 – 6y + 9
20y =-40
or y = -2
Substituting the value of y in equation (1), we get;
-6x = 2y – 14
-6x = -4 – 14 = -18
x = 3
Hence, the centre of the circle located at point (3,-2).