### Home > A2C > Chapter 8 > Lesson 8.2.3 > Problem8-149

8-149.

Complete the square to change $3x^{2} + 6x + 3y^{2} − 18y − 45 \lt 0$ to graphing form. Identify key points. Find the domain and range. Sketch the graph.

$3\left(x^{2} + 2x\right) + 3\left(y^{2} − 6y\right) − 45 \lt 0$

$3\left(x + 1\right)^{2} + 3\left(y − 3\right)^{2} − 75 \lt 0$

Divide by $3$, then simplify.

$\text{Radius} = \sqrt{25} = 5$
$\text{Domain} = −6 \lt x \lt 4$
$\text{Range} = −2 \lt y \lt 8$