Circle has the equation x 2 + y 2 - 6 x + 10 y...

A two-dimensional number line, such as two perpendicular number lines oraxes, can be thought of as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.

The standard equation of a circle, center ${\displaystyle C=(h,k)}$ and radius ${\displaystyle =r}$ is
${\displaystyle {(x-h)}^2+{(y-k)}^2=r^2}$
Complete the square to change the given equation to standard form.
${\displaystyle x^2+y^2-6x+10y-15=0}$
${\displaystyle x^2-6x+y^2+10y=15}$
${\displaystyle x^2-6x+9+y^2+10y+25=15+9+25}$
${\displaystyle {(x-3)}^2+{(y+5)}^2=49=7^2}$
The center is ${\displaystyle =(3,-5)}$ and the radius is ${\displaystyle =7}$
The graph is as follows :
graph{x^2+y^2-6x+10y-15=0 [-14.8, 17.23, -12.3, 3.72]}