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2023-02-22

Circle has the equation ${x}^{2}+{y}^{2}-6x+10y-15=0$, how do you graph the circle using the center (h,k) radius r?

Helen Merritt

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.

Riley Cisneros

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

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