SOLUTION: find the equation of acircle given the center c(-4,6) passing through p(1,2)

Algebra ->  Circles -> SOLUTION: find the equation of acircle given the center c(-4,6) passing through p(1,2)      Log On


   

Question 654959: find the equation of acircle given the center c(-4,6) passing through p(1,2)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
We use the standard form the equation of the circle with C+%28h%2Ck%29 and
r is %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
given the center is C%28-4%2C6%29 and passes through the point P%28x%2Cy%29=+P%281%2C2%29
plug these values in:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
%281-%28-4%29%29%5E2%2B%282-6%29%5E2=r%5E2...solve for r
%281%2B4%29%5E2%2B%28-4%29%5E2=r%5E2
5%5E2%2B%28-4%29%5E2=r%5E2
25%2B16=r%5E2
r%5E2=41
or r=sqrt%2841%29
solving the equation of the circle
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
%28x%2B4%29%5E2%2B%28y-6%29%5E2=41
x%5E2%2B8x%2B16%2By%5E2-12y%2B36=41
x%5E2%2B8x%2By%5E2-12y%2B52=41
x%5E2%2B8x%2By%5E2-12y=41-52
x%5E2%2B8x%2By%5E2-12y=-11..........answer
graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2C+x%5E2%2B8x%2By%5E2-12y%3C=-11%29