Answer:
Center (-5/2, 1/2)
Radius = √(9/2)
Step-by-step explanation:
First, convert the equation to the standard form of the equation of a circle.
[tex] {x}^{2} + {y}^{2} + 5x - y + 2 = 0 \\ {x}^{2} + 5x + {y}^{2} - y + 2 = 0 \\ {x}^{2} + 5x + {( \frac{5}{2}) }^{2} - {( \frac{5}{2} )}^{2} + {y}^{2} - y + {( - \frac{ 1}{2} )}^{2} - {( - \frac{1}{2}) }^{2} + 2 = 0 \\ {(x + \frac{5}{2}) }^{2} - \frac{25}{4} + {(y - \frac{1}{2}) }^{2} - \frac{1}{4} + 2 = 0 \\ {(x + \frac{5}{2}) }^{2} + {(y - \frac{1}{2} )}^{2} = \frac{9}{2} [/tex]
Compare with the standard equation,
[tex] {(x - a})^{2} + {(y - b)}^{2} = {r}^{2} [/tex]
Center (a, b) = (-5/2, 1/2)
r² = 9/2
Radius, r = √(9/2)
