Chapter 13, Problem 25RP

To determine

To find: The description for the graph of the given equation.

Answer to Problem 25RP

Theequation is the equation of the circle with the centre of the circle is $\left(-1,3\right)$ and the radius of the circle is 0.

Explanation of Solution

Given:

The give equation is $x^2+2x+y^2-6y=-10$ .

Calculation:

Consider the given equation is $x^2+2x+y^2-6y=-10$ .

Solve the given equation as,

  $\begin{array}{l}{x}^2+2x+y^2-6y+1+9=-10+1+9\\ {\left(x+1\right)}^2+{\left(y-3\right)}^2=0\end{array}$

The general form for the equation of the circle is,

  ${\left(x^2-h\right)}^2+{\left(y-k\right)}^2=r^2$

The equation is the equation of the circle with the centre of the circle is $\left(-1,3\right)$ and the radius of the circle is 0.