Cylinders & Quadric Surfaces

Find the correct equation for the graph.

• $z=\cos\left(x\right)$

• $z=\cos\left(y\right)$

• $z=\sin\left(x\right)$

• $z=\sin\left(y\right)$

Choose the equation that describe this surface.

• $\frac{x^2}{4}+\frac{y^2}{9}+\frac{z^2}{16}=1$

• $\frac{x^2}{2}+\frac{y^2}{3}+\frac{z^2}{4}=1$

• $\frac{x^2}{9}+\frac{y^2}{4}+\frac{z^2}{16}=1$

• $\frac{x^2}{3}+\frac{y^2}{2}+\frac{z^2}{4}=1$

Choose the correct equation for the graph.

• $\frac{x^2}{16}+\frac{y^2}{4}-\frac{z^2}{9}=1$

• $\frac{x^2}{4}+\frac{y^2}{16}-\frac{z^2}{9}=1$

• $\frac{x^2}{4}+\frac{y^2}{9}-\frac{z^2}{16}=1$

Choose the correct equation for the graph.

• $-\frac{x^2}{16}+\frac{y^2}{9}-\frac{z^2}{9}=1$

• $\frac{x^2}{16}-\frac{y^2}{9}-\frac{z^2}{9}=1$

• $-\frac{x^2}{16}-\frac{y^2}{9}+\frac{z^2}{9}=1$

Find the correct equation that describe the graph.

•  $\frac{\left(x-1\right)^2}{4}\ +\frac{z^2}{16}=\frac{\left(y-2\right)^2}{9}$  

•  $\frac{\left(x+1\right)^2}{4}\ +\frac{z^2}{16}=\frac{\left(y+2\right)^2}{9}$  

•  $\frac{\left(x-2\right)^2}{4}\ +\frac{z^2}{16}=\frac{\left(y-1\right)^2}{9}$  

•  $\frac{\left(x+2\right)^2}{4}\ +\frac{z^2}{16}=\frac{\left(y+1\right)^2}{9}$  

Find the best description for the graph.

• Elliptical paraboloid  $y^2+\frac{z^2}{4}=-\frac{x}{2}$  

• Elliptical paraboloid $\frac{y^2}{4}+z^2=-\frac{x}{2}$  

• Circular paraboloid  $y^2+z^2=-\frac{x}{2}$  

What is the intersection of  $\frac{x^2}{9}-\frac{z^2}{25}=\frac{y}{2}$  and  $x=0$  ?

• Both parabola and hyperbola

• A hyperpola

• A parabola