SOLUTION: For the following general form of a circle, find the value of "a" if the center is at (1/3, 4/3). Use this value of "a" to find the radius of a circle. Make sure to write it in s

Question 606483: For the following general form of a circle, find the value of "a" if the center is at (1/3, 4/3). Use this value of "a" to find the radius of a circle. Make sure to write it in simplified rationalized form.
3x^2-2x+3y^2-ay-27=0
I know you would group it just as you would any other equation when you are going from general to standard, but I am confused as to what to do with the -ay. Help please.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
For the following general form of a circle, find the value of "a" if the center is at (1/3, 4/3). Use this value of "a" to find the radius of a circle. Make sure to write it in simplified rationalized form.
3x^2-2x+3y^2-ay-27=0
complete the square
3(x^2-2x/3+1/9)+3(y^2-ay+a^2/4)=27+1/3+3/2=27+11/6
3(x-1/3)^2+3(y-a/2)^2=173/6
a/2=4/3
a=8/3
equation of given circle:
3(x-1/3)^2+3(y-4/3)^2=173/6
radius^2=173/6
radius=√(173/6)=√1038/6
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