\( 1<\begin{array}{l}\text { Write the standard form of the equation and the general form of the equation of the cirele witl } \\ \text { radius r and center }(h, k) \text {. Then graph the eirele. } \\ r=2 ; \quad(h, k) \equiv(-2,0) \\ \text { The standard form of the equation of this cirele is }(x+2)^{2}+y^{2}=4 \text {. } \\ \text { The general form of the equation of this cirele is } \\ \text { (Simplify your answer.) }\end{array} \)

The general form of the equation of the circle can be derived from the standard form \((x + 2)^2 + y^2 = 4\). To convert it to general form, expand the terms: \[ (x + 2)^2 + y^2 = 4 \quad \Rightarrow \quad x^2 + 4x + 4 + y^2 = 4 \] Now, subtract 4 from both sides: \[ x^2 + y^2 + 4x + 4 - 4 = 0 \] Thus, the general form is: \[ x^2 + y^2 + 4x = 0 \] When graphing the circle, center it at the point \((-2, 0)\) and draw a circle with a radius of 2, extending to points such as \((-4,0)\), \((0,0)\), and \((-2, 2)\). It’s a delightful exercise that brings the concept of circles to life on the coordinate plane! To avoid common mistakes when graphing circles, remember the relationship between the center and radius: ensure you measure two units outward from the center point in all directions. A handy tip is to plot key points beforehand—this will help you visualize the circle and ensure it is symmetric!