91Ó°ÊÓ

Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, ellipses, and hyperbolas. $$ x=\frac{1}{2}(y-1)^{2}-2 $$

Use a graphing calculator to graph each equation. (Hint: Solve for \(y\) and graph two functions.) See Using Your Calculator: $$ x^{2}+y^{2}=5 $$

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} x y=-\frac{9}{2} \\ 3 x+2 y=6 \end{array}\right. $$

Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, and ellipses. $$ 16(x-5)^{2}+25(y-4)^{2}=400 $$

Graph the ellipses described by the equations in parts a and \(b\) on the same coordinate system. a. \(\frac{x^{2}}{9}+\frac{y^{2}}{25}=1\) b. \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\)

Use a graphing calculator to graph each equation. (Hint: Solve for \(y\) and graph two functions.) See Using Your Calculator: $$ (x+1)^{2}+y^{2}=16 $$

Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, ellipses, and hyperbolas. $$ \frac{y^{2}}{25}-\frac{(x-2)^{2}}{4}=1 $$

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} x^{2}-2 y^{2}=6 \\ x^{2}+2 y^{2}=2 \end{array}\right. $$

Graph the ellipses described by the equations in parts a and \(b\) on the same coordinate system. a. \(\frac{x^{2}}{169}+\frac{y^{2}}{25}=1\) b. \(\frac{x^{2}}{25}+\frac{y^{2}}{169}=1\)

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} x^{2}+9 y^{2}=1 \\ x^{2}-9 y^{2}=3 \end{array}\right. $$