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How do you determine the center and radius of a circle with equation x2 plus y2 plus 10x minus 6y equals 0?
A circle with centre (x0, y0) and radius r has an equation of the form:
(x - x0)2 + (y - yo)2 = r2
To get into this form, first reorder to separate the variables:
x2 + y2 + 10x - 6y = x2 + 10x + y2 - 6y
Second complete the square in each variable:
x2 + 10x = (x + 5)2 - 25
y2 - 6y = (y - 3)2 - 9
Third substitute back in the equation and rearrange:
(x + 5)2 - 25 + (y - 3)2 - 9 = 0
(x + 5)2 + (y - 3)2 = 34
The centre and radius of the circle can now be read from the equation:
Centre = (-5, 3)
Radius = sqrt(34)
What else can I help you with?
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What is the equation for a circle with its center at the origin and a tangent whose equation is y equals 7?
x2 + y2 = 49
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