The circle x^2 y^2 2gx 2fy c=0 passes through the points A(-1,-2),B(1,2)and C(2,3). Write down three equation which must satisfied g,f,c.
To find the equations that must be satisfied by g, f, and c, we can use the given information about the circle passing through points A(-1, -2), B(1, 2), and C(2, 3).
Step 1: Substitute the given points A(-1, -2), B(1, 2), and C(2, 3) into the general equation of a circle to get a system of three equations.
1) For point A:
(-1)^2 (-2)^2 2g(-1) 2f(-2) c = 0
4g + 8f + c = 0
2) For point B:
(1)^2 (2)^2 2g(1) 2f(2) c = 0
4g + 16f + c = 0
3) For point C:
(2)^2 (3)^2 2g(2) 2f(3) c = 0
36g + 54f + c = 0
These three equations must be satisfied by g, f, and c for the circle to pass through the points A, B, and C.