Find the equation of the circle passing through the point (-2, 8), (7, -1) and (1, 2)
Answers
The equation of the circle is x² + y² -17x -19y + 50 = 0
Given:
The circle passes through the points (-2,8), (7,-1) and (1,2)
To find:
Equation of the circle
Solution:
Let the equation of the circle be x² + y² + 2gx + 2fy + c = 0
Since it passes through (-2,8),
we get (-2)² + (8)² + 2g(-2) + 2f(8) + c = 0
=> 4 + 64 -4g + 16f + c = 0
=> 68 - 4g + 16f + c = 0 _____________equation (i)
For (7, -1), we get the equation:
=> (7)² + (-1)² + 2g(7) + 2f(-1) + c = 0
=> 49 + 1 + 14g -2f + c = 0
=> 50 + 14g -2f + c = 0 _____________equation (ii)
For (1,2), we get the equation:
=> (1)² + (2)² + 2g(1)+ 2f(2) + c = 0
=> 1 + 4 + 2g + 4f + c = 0
=> 5 + 2g + 4f + c = 0 _____________equation (iii)
On solving equations (i), (ii) and (iii), we get:
c = 50
f = -19/2
g = -17/2
Substituting the values of c, f and g in the equation of circle:
x² + y² + 2(-17/2)x + 2(-19/2)y + 50 = 0
x² + y² -17x -19y + 50 = 0
Therefore, the equation of the required circle is x² + y² -17x -19y + 50 = 0
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