91Ó°ÊÓ

a. The graphs of the two independent equations of a system are parabolas. How many solutions might the system have? b. The graphs of the two independent equations of a system are hyperbolas. How many solutions might the system have?

Write the equation \(x^{2}-y^{2}-2 x+4 y=12\) in standard form to show that it describes a hyperbola.

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ x=\frac{1}{2} y^{2}+2 y $$

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ x=-\frac{1}{3} y^{2}-2 y $$

$$ \text { Solve the system for real solutions: }\left\\{\begin{array}{l} \frac{1}{x}+\frac{2}{y}=1 \\ \frac{2}{x}-\frac{1}{y}=\frac{1}{3} \end{array}\right. $$

Write the equation \(x^{2}-4 y^{2}+2 x-8 y=7\) in standard form to show that it describes a hyperbola.

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ y=-4(x+5)^{2}+5 $$

$$ \text { Solve the system for real solutions: }\left\\{\begin{array}{l} \frac{1}{x}+\frac{3}{y}=4 \\ \frac{2}{x}-\frac{1}{y}=7 \end{array}\right. $$

Write the equation \(36 x^{2}-25 y^{2}-72 x-100 y=964\) in standard form to show that it describes a hyperbola.

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ y=-4(x-4)^{2}-4 $$