Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.

$$9 y^2+18 y=25 x^2+216$$

Find the distance between the pair of points with the given coordinates.

$$(-4,9),(1,-3)$$

Find the exact solution(s) of the system of equations.

$$\begin{aligned} & 3 x^2-20 y^2-12 x+80 y-96=0 \\ & 3 x^2+20 y^2=80 y+48 \end{aligned}$$

Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation. Then graph the hyperbola.

$$\frac{x^2}{9}-\frac{y^2}{25}=1$$

There is an open area south of the White House known as the Ellipse. Write an equation to model the Ellipse. Assume that the origin is at the center of the Ellipse.

Find the exact solution(s) of the system of equations.

$$\begin{aligned} & x^2-y^2-12 x+12 y=36 \\ & x^2+y^2-12 x-12 y+36=0 \end{aligned}$$

Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.

$$x^2-8 y+y^2+11=0$$

Find the exact solution(s) of the system of equations.

$$\begin{aligned} & 2 x^2+8 y^2+8 x-48 y+30=0 \\ & 2 x^2-8 y^2=-48 y+90 \end{aligned}$$

Write an equation for the circle that satisfies the set of conditions.

center $(-\sqrt{13}, 42)$, passes through the origin

Use the following information. The U.S. Geological Survey (USGS) has determined the official center of the continental United States.

How does the location given by USGS compare to the result of your method?

Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation. Then graph the hyperbola.

$$\frac{y^2}{16}-\frac{x^2}{25}=1$$

At its closest point, Mars is 128.5 million miles from the Sun. At its farthest point, Mars is 155.0 million miles from the Sun. Write an equation for the orbit of Mars. Assume that the center of the orbit is the origin, the Sun lies on the $x$-axis, and the radius of the Sun is 400,000 miles.

Which of the following is NOT a role of the Federal Reserve System? A. controlling bank reserves B. printing currency (Federal Reserve notes) C. carrying out monetary policy D. supervising and regulating banks E. holding reserves for commercial banks

Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation. Then find the length of the latus rectum and graph the parabola.

$$x=y^2-14 y+25$$