Question

Determine the center and radius of the following circle equation: x² + y2 + 4x – 6y + 9 = 0 Center: Radius:

Answer 1

The center of the circle is (2,-3) while the radius of the circle is 2 units

Here, we want to determine the center and the radius of the given circle

Generally, we have the equation of a circle as follows;

`(x-a)^2+(y-b)^2=r^2`

Where (a,b) represents the center of the circle and r is the radius of the circle

We have this as follows by dividing the coefficients of x and y by 2

`\begin{gathered} (x+2)^2+(y-3)^2-4\text{ = 0} \\ \text{where (x+2)}^2=x^2+4x\text{ + 4} \\ (y-3)^2=y^2-6y+9 \\ By\text{ subtracting 4 from the sum 13, we have -4} \\ so\text{ we have;} \\ (x+2)^2+(y-3)^2\text{ = 4} \\ (x+2)^2+(y-3)^2=2^2 \end{gathered}`

The center of the circle is (2,-3) while the radius of the circle is 2 units