91Ó°ÊÓ

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

The graph of each equation is a circle. Find the center and the radius, and then sketch. See Examples \(5,6,\) and \(8 .\) $$ x^{2}+y^{2}-2 x-6 y-5=0 $$

Identify whether each equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of each equation. \(y=x^{2}+12 x+36\)

Write an equation of the circle with the given center and radius. See Example 7. $$ (2,3) ; 6 $$

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

Identify whether each equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of each equation. \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\)

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} x^{2}+y^{2} &=25 \\ x &=y^{2}-5 \end{aligned}\right. $$

Identify whether each equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of each equation. \(\frac{y^{2}}{9}-\frac{x^{2}}{9}=1\)

Write an equation of the circle with the given center and radius. See Example 7. $$ (-7,6): 2 $$

Identify whether each equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. Sketch the graph of each equation. \(\frac{x^{2}}{16}-\frac{y^{2}}{4}=1\)