Question

Discuss the equation $x^2+y^2-2x+4y-4=0$. Graph it.

Short answer

The graph of the equation is

Step-by-step solution

Step 1. Given Information

We are given the equation $x^2+y^2-2x+4y-4=0$and we need to graph the equation.

Step 2. Simplifying the equation

The standard form of the equation of a circle is${(x-h)}^2+{(y-k)}^2=r^2$.

Simplifying the given equation we get:

role="math" localid="1646386481597" $$\begin{gathered} \Rightarrow x^2+y^2-2x+4y-4=0 \\ \Rightarrow x^2-2x+1+y^2+4y+4=1+4+4 \\ \Rightarrow {(x-1)}^2+{(y+2)}^2=9 \\ \Rightarrow {(x-1)}^2+{(y+2)}^2={\left(3\right)}^2 \end{gathered}$$

Comparing the equation with the standard form we get the center of the circle is at$(1,-2)$and radius is$3$units.

Step 3. Plotting the graph

The graph of the equation is: