Eqation of a Circle From Three Points

[dylanwebb97]

Here is the problem that I need help with.

To find the circle through the points P(5, 3), Q(23, 3), and R(3, 23), follow these steps. Think of P, Q, and R as the vertices of a triangle.

1. Find the midpoint of PQ.
2. Find the slope of PQ and the slope of the line perpendicular to PQ.
3. Find the equation of the perpendicular bisector of PQ.
4. Repeat steps 1 through 3 for QR.
5. Find the point of intersection of the perpendicular bisectors of PQ and QR. Call this point C, the center of the circle.
6. Find CP = CQ = CR. The distance from C to each of these points is the radius of the circle.
7. Use the coordinates of C and the radius of the circle to write the equation of the circle. Show that P, Q, and R are points on the circle by showing that their coordinates make the equation of the circle true.

I need help with the slopes of PQ and QR.

 

[Deleted member 4993]

Here is the problem that I need help with.

To find the circle through the points P(5, 3), Q(23, 3), and R(3, 23), follow these steps. Think of P, Q, and R as the vertices of a triangle.

1. Find the midpoint of PQ.
2. Find the slope of PQ and the slope of the line perpendicular to PQ.
3. Find the equation of the perpendicular bisector of PQ.
4. Repeat steps 1 through 3 for QR.
5. Find the point of intersection of the perpendicular bisectors of PQ and QR. Call this point C, the center of the circle.
6. Find CP = CQ = CR. The distance from C to each of these points is the radius of the circle.
7. Use the coordinates of C and the radius of the circle to write the equation of the circle. Show that P, Q, and R are points on the circle by showing that their coordinates make the equation of the circle true.

I need help with the slopes of PQ and QR.

If a line is drawn through two points P (x₁, y₁) and Q(x₂, y₂) then the slope of the line is:

m = (y₁ - y₂)/(x₁ - x₂)