ex2.1_11

$x^2+y^2+2x-4y-4=0$ describes a circle. Write the equation in standard form and determine the center and radius of the circle.

$x$ $y$ -variables.

x^2+y^2+2x-4y-4=0\\[0.25 in] x^2+2x \quad + \quad y^2-4y \quad = \quad 4\\[0.25 in] x^2+2x+1 \quad + \quad y^2-4y+4 \quad = \quad 4 + 1 + 4\\[0.25 in] (x+1)^2 + (y-2)^2 = 9

The original equation is now written in standard form. We can read the center and radius:

(h,k)=(-1,2)\\[0.25 in] r=3.