SOLUTION: write the equation of a circle given the following information. a. center (2,3) point (-3,-9) b. endpoints (2,5) and (2,13)

Algebra ->  Circles -> SOLUTION: write the equation of a circle given the following information. a. center (2,3) point (-3,-9) b. endpoints (2,5) and (2,13)      Log On


   

Question 444943: write the equation of a circle given the following information.
a. center (2,3) point (-3,-9) b. endpoints (2,5) and (2,13)
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
a)To determine the equation of the circle we need the center and radius. Since its center is given (2, 3), we calculate the radius:
r=sqrt%28%28-3-2%29%5E2%2B%28-3-2%29%5E2%29=sqrt%28169%29=13. Now we write the equation of the
circle centered at (2, 3) and passes through (-3, -9):
%28x-2%29%5E2%2B%28y-3%29%5E2=169.
b)Since we know the endpoints of diameter the center will be:
X=%282%2B2%29%2F2=2 and Y=%285%2B13%29%2F2=9 the point (2, 9)
To find the radius we find the half of diameter:
r=d%2F2=%28sqrt%28%282-2%29%5E2%2B%2813-5%29%5E2%29%29%2F2=4 and the equation will be:
%28X-2%29%5E2%2B%28Y-9%29%5E2=16