Chapter 13

Graph each hyperbola. $$ \frac{x^{2}}{36}-\frac{y^{2}}{36}=1 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ y=x^{2}+4 x-5 $$

Graph each inequality. $$ \frac{x^{2}}{25}+\frac{y^{2}}{4} \geq 1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{r} 6 x-y=5 \\ x y=1 \end{array}\right. $$

Graph each hyperbola. $$ \frac{y^{2}}{25}-\frac{x^{2}}{16}=1 $$

Graph each inequality. $$ \frac{y^{2}}{4}-x^{2} \leq 1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=2 x^{2}+1 \\ x+y=-1 \end{array}\right. $$

Graph each hyperbola. $$ \frac{y^{2}}{25}-\frac{x^{2}}{49}=1 $$

Graph each inequality. $$ \frac{y^{2}}{16}-\frac{x^{2}}{9}>1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=9 \\ x+y=5 \end{array}\right. $$

Graph each hyperbola. $$ x^{2}-4 y^{2}=16 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}=9 $$

Graph each inequality. $$ y<(x-2)^{2}+1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=x^{2}-4 \\ y=x^{2}-4 x \end{array}\right. $$

Graph each hyperbola. $$ 4 x^{2}-y^{2}=36 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}=25 $$

Graph each inequality. $$ y>(x-2)^{2}+1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x=y^{2}-3 \\ x=y^{2}-3 y \end{array}\right. $$

Graph each hyperbola. $$ 16 y^{2}-x^{2}=16 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+(y-2)^{2}=1 $$

Graph each inequality. $$ y \leq x^{2}+x-2 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} 2 x^{2}+3 y^{2}=14 \\ -x^{2}+y^{2}=3 \end{array}\right. $$

Graph each hyperbola. $$ 4 y^{2}-25 x^{2}=100 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ (x-3)^{2}+y^{2}=9 $$

Graph each inequality. $$ y>x^{2}+x-2 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} 4 x^{2}-2 y^{2}=2 \\ -x^{2}+y^{2}=2 \end{array}\right. $$

Graph each equation. $$ \frac{y^{2}}{36}=1-x^{2} $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ (x-5)^{2}+(y+2)^{2}=1 $$

Graph each system. $$ \left\\{\begin{array}{r} 4 x+3 y \geq 12 \\ x^{2}+y^{2}<16 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{r} x^{2}+y^{2}=1 \\ x^{2}+(y+3)^{2}=4 \end{array}\right. $$

Graph each equation. $$ \frac{x^{2}}{36}=1-y^{2} $$

Graph each system. $$ \left\\{\begin{array}{r} 3 x-4 y \leq 12 \\ x^{2}+y^{2}<16 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+2 y^{2}=4 \\ x^{2}-y^{2}=4 \end{array}\right. $$

Graph each equation. $$ 4(x-1)^{2}+9(y+2)^{2}=36 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}+6 y=0 $$

Graph each system. $$ \left\\{\begin{array}{l} x^{2}+y^{2} \leq 9 \\ x^{2}+y^{2} \geq 1 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=x^{2}+2 \\ y=-x^{2}+4 \end{array}\right. $$

Graph each equation. s$$ 25(x+3)^{2}+4(y-3)^{2}=100 $$

Graph each system. $$ \left\\{\begin{array}{l} x^{2}+y^{2} \geq 9 \\ x^{2}+y^{2} \geq 16 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x=-y^{2}-3 \\ x=y^{2}-5 \end{array}\right. $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+10 x+y^{2}=0 $$

Graph each equation. $$ 8 x^{2}+2 y^{2}=32 $$

Graph each system. $$ \left\\{\begin{array}{l} y>x^{2} \\ y \geq 2 x+1 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} 3 x^{2}+y^{2}=9 \\ 3 x^{2}-y^{2}=9 \end{array}\right. $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}+2 x-4 y=4 $$

Graph each equation. $$ 3 x^{2}+12 y^{2}=48 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}+6 x-4 y=3 $$

Graph each system. $$ \left\\{\begin{array}{l} y \leq-x^{2}+3 \\ y \leq 2 x-1 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=25 \\ x=y^{2}-5 \end{array}\right. $$

Graph each equation. $$ 25 x^{2}-y^{2}=25 $$