SOLUTION: Find the center, radius and intercepts of the circle with the given equations. 3x^2+3y^2-18x+24y+27 =0

Algebra ->  Graphs -> SOLUTION: Find the center, radius and intercepts of the circle with the given equations. 3x^2+3y^2-18x+24y+27 =0       Log On


   

Question 714398: Find the center, radius and intercepts of the circle with the given equations. 3x^2+3y^2-18x+24y+27 =0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B3y%5E2-18x%2B24y%2B27=0 --> x%5E2%2By%5E2-6x%2B8y%2B9=0 (dividing both sides of the equal sign by 3)
Look at the terms in x,
Since x%5E2+-6x is part of %28x-3%29%5E2=x%5E2-2%2A3x%2B3%5E2=x%5E2-6x%2B9 we can "complete the square"
with the 9 already present at the end of the equation.
Now, look at the terms in y,
y%5E2%2B8y is part of y%5E2%2B8y%2B4%5E2=+%28x%2B4%29%5E2 ,
so adding 4%5E2 to both sides of the equal sign in x%5E2%2By%5E2-6x%2B8y%2B9=0 we can rearrange and group to get
x%5E2%2By%5E2-6x%2B8y%2B9%2B4%5E2=4%5E2-->x%5E2-6x%2B9%2By%5E2%2B8y%2B4%5E2=4%5E2-->%28x%5E2-6x%2B9%29%2B%28y%5E2%2B8y%2B4%5E2%29=4%5E2-->highlight%28%28x-3%29%5E2%2B%28y%2B4%29%5E2=4%5E2%29
That is the equation of a circle of radius highlight%284%29 centered at (3,-4),
the point with highlight%28x=3%29 and highlight%28y=-4%29