Write the equation $10 x^2+2 y^2=40$ in standard form.

Where do the graphs of the equations $y=2 x+1$ and $2 x^2+y^2=11$ intersect?

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.

$$y=3 x^2-24 x+50$$

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.

$$x=5 y^2+25 y+60$$

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

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

Solve the system of inequalities by graphing.

$$\begin{aligned} & x^2-y^2 \geq 1 \\ & x^2+y^2 \leq 16 \end{aligned}$$

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.

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

center at $(-8,-7)$, tangent to $y$-axis

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 distance between the pair of points with the given coordinates.

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

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.

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

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

endpoints of a diameter at $(9,4)$ and $(-3,-2)$

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

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

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.

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