Question 1183725: A circle through P(5,9), Q(11,-3), and R(13,3). Find its equation in standard form, by doing the following steps.
a. Determine an equation of the perpendicular bisector of the segment PR.
b. Determine an eqution of the perpendicular bisector of QR.
c. The perpendicular bisector of any chord of a circle will pass through the center. Thus, find the intersection of the two perpendicular bisectors above. This will be the center C of the circle.
d. To find the circle's radius, find the distance of C from any of the three points P,Q, or R. You may use any of these three points?
e. What is the standard equation of the circle?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The problem tells you exactly what to do; all of the steps are elementary. If you are having difficulty with any of the steps, then re-post the problem, telling us what those difficulties are. If you are just expecting us to do all your work for you, then don't bother re-posting; that's not what we are here for.
a,b: to find the equation of the perpendicular bisector of each segment...
(1) find the slope m and midpoint (a,b) of the given segment
(2) find the slope of the line perpendicular to the given segment -- -1/m, the negative reciprocal of the slope of the given segment
(3) use the midpoint (a,b) and the slope -1/m in the point-slope form of the equation:
c: to find the intersection of the two perpendicular bisectors, solve the pair of equations for those lines simultaneously (solve a system of two linear equations)
d: distance formula....
e: if the center is (h,k) and the radius is r, the equation is
|
|
|
