The radius of a the circle whose equation is x² + y² - 10x + 6y + 18 = 0 is 4.
Equation of a circle
The equation of a circle can be described as follows:
(x - h)² + (y - k)² = r²
where
- h and k are the centre
- r = radius
Therefore,
x² + y² - 10x + 6y + 18 = 0
Therefore,
x² - 10x + y² + 6y + 18 = 0
(x² - 10x + 25) + (y² + 6y + 9) + 18 = 25 + 9
(x - 5)² + (x + 3)² + 18 = 25 + 9
subtract 18 from both sides
(x - 5)² + (x + 3)² = 16
r² = 16
r = √16
r = 4
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