Determine whether the statement is true or false. Justify your answer.

The graph of $x^2+4y^4-4=0$ is an ellipse.

In this exercise, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola.

$$3 x^2=12+3 y^2$$

Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.

$$3.2x^2= 2.1y(1 - 2y)$$

Graph the below given ellipse and also label the center and vertices :

$$x^2 - 2x + 2y^2 - 4y - 5 = 0$$

Find the center and vertices of the ellipse, and sketch its graph.

$$25 x^{2}+4 y^{2}-50 x-24 y-39=0$$

For the following exercises, graph the ellipse, noting center, vertices, and foci. $\frac{x^{2}}{36}+\frac{y^{2}}{9}=1$

Find the center and vertices of the ellipse, and sketch its graph.

$$25 x^{2}+9 y^{2}-200 x+54 y+256=0$$

In this exercise, indicate whether the graph of the given equation is a circle, an ellipse, a hyperbola, or a parabola.

$$36 y^2=576+16 x^2$$

Find the center and vertices of the ellipse, and sketch its graph.

$$9 x^{2}+4 y^{2}-36 x+8 y+31=0$$

Find the vertices and the foci of the ellipse. Then draw the graph.

$\frac{(x-2)^2}{16}+\frac{(y+1)^2}{4}=1$.

Find an equation for the conic section with the given properties.

The ellipse with foci $F_1(1,1)$ and $F_2(1,3)$ and with one vertex on the $x$-axis

Find the center and vertices of the ellipse, and sketch its graph.

$$25 x^{2}+16 y^{2}-150 x-128 y+81=0$$

Graph each ellipse. Give the domain and range. $\frac{(x-8)^{2}}{100}+\frac{(y-5)^{2}}{49}=1$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. See the previous examples.

$$-x^2+5 y^2=3$$