Answer:
Step-by-step explanation:
Perpendicular bisector of the chord connecting the the points (-1,2) and (2,3) is also passing through the center of the circle.
We'll find the equation of the line and solve the system to find the center.
Midpoint of the chord:
- ((-1 + 2)/2, (2 + 3)/2) = (0.5, 2.5)
Equation of the line through chord (-1,2) and (2,3):
- m = (3 - 2)/(2 + 1) = 1/3
- y - 2 = 1/3(x + 1)
- y = 1/3x + 7/3
Perpendicular bisector is:
- y - 2.5 = -3(x - 0.5)
- y = -3x + 4 >> (1)
And the given line is:
- 2x - 3y + 1 = 0
- y = 2/3x + 1/3 >> (2)
Solve the system:
- -3x + 4 = 2/3x + 1/3
- -9x + 12 = 2x + 1
- 11x = -11
- x = -1
Find y:
- y = -3(-1) + 4 = 3 + 4 = 7
The center is (-1, 7)
Find the radius, the distance from center to one of points on circle
- (-1, 7) and (-1, 2)
- 7 - 2 = 5
The equation of circle is:
- (x + 1)² + (y - 7)² = 5²
- (x + 1)² + (y - 7)² = 25
