SOLUTION: 1.find the equation of the circle w/ center (1, 4) and radius 5. 2.find the equation of the circle w/ center (-3, 6) and radius 4. 3.reduce the equation to standard form and fin

Algebra ->  Expressions-with-variables -> SOLUTION: 1.find the equation of the circle w/ center (1, 4) and radius 5. 2.find the equation of the circle w/ center (-3, 6) and radius 4. 3.reduce the equation to standard form and fin      Log On


   

Question 936879: 1.find the equation of the circle w/ center (1, 4) and radius 5.
2.find the equation of the circle w/ center (-3, 6) and radius 4.
3.reduce the equation to standard form
and find the center and radius of the circle.
a. x^2+y^2+4x-6y-12=0
b.x^2+y^2-8x+2y-16=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation for a circle centered at (h,k) with radius R is,
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
1. %28x-1%29%5E2%2B%28y-4%29%5E2=25
Now do the same for 2.
.
.
.
To get to the general equation, complete the square in x and y,
+x%5E2%2B4x%2By%5E2-6y=12
+%28x%5E2%2B4x%2B4%29%2B%28y%5E2-6y%2B9%29=12%2B4%2B9
%28x%2B2%29%5E2%2B%28y-3%29%5E2=25
(-2,3), R=5
.
.
.
x%5E2-8x%2By%5E2%2B2y=16
%28x%5E2-8x%2B16%29%2B%28y%5E2%2B2y%2B1%29=16%2B16%2B1
%28x-4%29%5E2%2B%28y%2B1%29%5E2=33
(4,-1), R=sqrt%2833%29