Question 539195: A circle is Defined by the following equation,
3x^2+3y^2-30x+27=0.
what is the radius?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The equation for a circle in standard form is:
(x-a)^2 + (y-b)^2 = R^2
First, we can divide through by 3 which gives:
x^2 + y^2 - 10x + 9 = 0
In this case, we know b=0 since there is no linear term in y
The coefficient of the linear x term is -10, which is obtained from (x-5)(x-5)
So we can write
(x-5)^2 + y^2 = R^2
x^2 - 10x + 25 - R^2 + y^2 = 0 <-> x^2 - 10x + 9 + y^2 = 0
This means 25 - R^2 = 9 -> R^2 = 16
So the radius, R = 4
And the equation in standard form is:
(x-5)^2 + y^2 = 16
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