SOLUTION: Write the standard from of the equation and the general form of the equation of each circle of radius r and center (h,k);graph each circle. The problem says: r=4; (h,k)=(2,-3)

Algebra ->  Graphs -> SOLUTION: Write the standard from of the equation and the general form of the equation of each circle of radius r and center (h,k);graph each circle. The problem says: r=4; (h,k)=(2,-3)      Log On


   

Question 54388This question is from textbook College Algebra
: Write the standard from of the equation and the general form of the equation of each circle of radius r and center (h,k);graph each circle.

The problem says: r=4; (h,k)=(2,-3) This question is from textbook College Algebra

Found 3 solutions by stanbon, funmath, Nate:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write the standard from of the equation and the general form of the equation of each circle of radius r and center (h,k);graph each circle.
(x-h)^2 + (y-k)^2 = r^2
-------------
The problem says: r=4; (h,k)=(2,-3)
(x-2)^2 + (y+3)^2 = 16
Cheers,
Stan H.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Standard Form of the Equation of a Circle:highlight%28%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2%29
Where (h,k) are the center of the cicle and r is the radius.
Your center is (2,-3) and r=4
%28x-2%29%5E2%2B%28y-%28-3%29%29%5E2=4%5E2
highlight%28%28x-2%29%5E2%2B%28y%2B3%29%5E2=16%29
General Form of the equation of the circle:highlight%28x%5E2%2By%5E2%2Bax%2Bbx=c%29
Expand the standard form and put it in order:
%28x-2%29%5E2%2B%28y%2B3%29%5E2=16
%28x-2%29%28x-2%29%2B%28y%2B3%29%28y%2B3%29=16

%28x%5E2-2x-2x%2B4%29%2B%28y%5E2%2B3y%2B3y%2B9%29=16
%28x%5E2-4x%2B4%29%2B%28y%5E2%2B6y%2B9%29=16
x%5E2%2By%5E2-4x%2B6y%2B4%2B9=16
x%5E2%2By%5E2-4x%2B6y%2B13=16
x%5E2%2By%5E2-4x%2B6y%2B13-13=16-13
highlight%28x%5E2%2By%5E2-4x%2B6y=3%29
Happy Calculating!!!

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
(x - 2)^2 + (y + 3)^2 = 16