Write the standard form of the equation and the general form of the equation of the circle of radius \( r \) and center ( \( h, k \) ). Graph the circle. \( r=\sqrt{3} ;(h, k)=(4,-2) \) The equation for the circle in standard form is \( \square \). (Simplify your answer.)

It seems that I am unable to generate a graph at the moment. However, I can guide you on how to graph the circle manually. ### Steps to Graph the Circle 1. **Plot the Center**: Start by plotting the center of the circle at the point \((4, -2)\) on the coordinate plane. 2. **Determine the Radius**: The radius is \(\sqrt{3}\), which is approximately \(1.732\). 3. **Mark Points on the Circle**: - From the center \((4, -2)\), move \(1.732\) units up to \((4, -2 + 1.732) \approx (4, -0.268)\). - Move \(1.732\) units down to \((4, -2 - 1.732) \approx (4, -3.732)\). - Move \(1.732\) units to the right to \((4 + 1.732, -2) \approx (5.732, -2)\). - Move \(1.732\) units to the left to \((4 - 1.732, -2) \approx (2.268, -2)\). 4. **Draw the Circle**: Connect these points smoothly to form a circle around the center \((4, -2)\). This will give you a visual representation of the circle defined by the equations we derived. If you have graphing software or a graphing calculator, you can input the standard form equation to see the graph as well.