SOLUTION: find the equation of the circle containing the points P(0,-3) and Q(4,0) and whose center is on the line x+2y=0

Question 1106797: find the equation of the circle containing the points P(0,-3) and Q(4,0) and whose center is on the line x+2y=0
Answer by ikleyn(52775) (Show Source): You can put this solution on YOUR website!
.

1.  You need to find the center of the circle (h,k) and its radius "r". Then the equation of the circle will be 

     +  = .


2.  The center of the circle is the intersection of the given line with the perpendicular bisector of the straight line segment 
    connecting the given points P and Q.



3.  Therefore your algorithm is as follows:

    a)  Determine the slope of the line connecting the given points P and Q.

    b)  Find the middle point R of the segment PQ.

    c)  Write the equation of the perpendicular line to the segment PQ  passing through the point R.

    d)  Find the intersection point of this line with the given line

        as the solution of the system of 2 equations in 2 unknowns.

    d)  This intersection point is the center of the circle.

        Having this intersection point, find the radius of the circle as the distance from the center to any of the two gfiven points.

That's all.

You can find examples of solutions to similar problem in the lesson
- Find the standard equation of a circle, Problem 1
in this site.

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