How would you determine the equation of the circle which passes through the points D(-5,-5), E(-5,15), F(15,15)?
Substitute each point to the equation of the circle, develop 3 equations, and substract the ones that have at least 1 coordinate common (
The equation of the circle:
Substitute for each given point:
So the equation of the circle becomes:
The circle's equation is
First we need to find the equation of two lines, each one perpendicular to the segments formed by a pair of the given points and passing through the midpoint of this pair of points.
Since points D and E (
Equation of Line DE, where
Equation of line 1 perpendicular to DE and passing through midpoint
Equation of Line EF, where
Equation of line 2 perpendicular to EF and passing through midpoint
Combining equations of lines 1 and 2 (
The distance between point C to any of the given points is equal to the circle's radius
In the formula of the equation of the circle: