Find the coordinates of the centre of the circle passing through the points(0,0) , (-2,1) , and (-3,2). Also find its radius
Answers
answer : x² + y² - 3x - 11y = 0
Let equation of circle is x² + y² + 2gx + 2fy + c = 0.
circle passing through the points (0,0) , (-2, 1) and (-3, 2).
putting (0,0) in equation, 0² + 0² + 2g × 0 + 2f × 0 + c = 0
=> c = 0.............(1)
putting (-2,1) in equation, (-2)² + 1² + 2g × -2 + 2f × 1 + c = 0
=> 5 - 4g + 2f + c = 0
putting equation (1),
5 - 4g + 2f = 0.............(2)
putting (-3, 2) in equation, (-3)² + 2² + 2g × -3 + 2f × 2 + c = 0
=> 13 - 6g + 4f + c = 0
putting equation (1),
13 - 6g + 4f = 0.............(3)
equations (2) and (3),
13 - 6g + 4f - 2(5 -4g + 2f) = 0
or, 13 - 6g + 4f - 10 + 8g - 4f = 0
or, 3 + 2g = 0 => g = -3/2
2f = 4g - 5 = 4 × -3/2 - 5 = -6 - 5 = -11
=> f = -11/2
equation is x² + y² + 2(-3/2)x + 2(-11/2)y + 0 = 0
or, x² + y² - 3x - 11y = 0