SOLUTION: Change the equation below to h,k form. Find the center and the radius of the circle. Then, Graph the circle. X^2+y^2-10x+2y+22=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Change the equation below to h,k form. Find the center and the radius of the circle. Then, Graph the circle. X^2+y^2-10x+2y+22=0      Log On


   



Question 727319: Change the equation below to h,k form. Find the center and the radius of the circle. Then, Graph the circle.
X^2+y^2-10x+2y+22=0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+y%5E+2+%2B+a+x+%2B+b+y+=+c+...standard form
given:
x%5E2%2By%5E2-10x%2B2y%2B22=0
x%5E2%2By%5E2-10x%2B2y=-22.........a=-10, b=2, c=-22
the center has coordinates (-a%2F2 , -b%2F2) and radius r such that r%5E2+=+c+%2B+%28a%2F2%29%5E+2+%2B+%28b%2F2%29+%5E2
so, you have
(-a%2F2 , -b%2F2)=(-%28-10%29%2F2 ,+-2%2F2)=(10%2F2,-2%2F2)=(5,-1)
the center is at (5,-1)
r%5E2+=+c+%2B+%28a%2F2%29%5E+2+%2B+%28b%2F2%29+%5E2
r%5E2+=+-22+%2B+%28-5%29%5E+2+%2B+%281%29+%5E2
r%5E2+=+-22+%2B25+%2B+1
r%5E2+=+-22+%2B26
r%5E2+=+4
r=2

Substitute the above into the original equation and write in the standard form of the equation of a circle:

%28x+-+h%29+%5E2+%2B+%28y+-+k%29+%5E2+=+r+%5E2+...h=5, k=-1, and r=2
%28x+-+5%29+%5E2+%2B+%28y+%2B1%29+%5E2+=+4+