91Ó°ÊÓ

What is a hyperbola?

In Exercises \(63-68\), sketch the function represented by the given parametric equations. Then use the graph to determine each of the following: a. intervals, if any, on which the function is increasing and intervals, if any, on which the function is decreasing. b. the number, if any, at which the function has a maximum and this maximum value, or the number, if any, at which the function has a minimum and this minimum value. $$x=2(t-\sin t), y=2(1-\cos t) ; 0 \leq t \leq 2 \pi$$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? $$\left\\{\begin{array}{l} x=(y+2)^{2}-1 \\ (x-2)^{2}+(y+2)^{2}=1 \end{array}\right.$$

In Exercises \(63-68\), sketch the function represented by the given parametric equations. Then use the graph to determine each of the following: a. intervals, if any, on which the function is increasing and intervals, if any, on which the function is decreasing. b. the number, if any, at which the function has a maximum and this maximum value, or the number, if any, at which the function has a minimum and this minimum value. $$x=3(t-\sin t), y=3(1-\cos t) ; 0 \leq t \leq 2 \pi$$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? $$\left\\{\begin{array}{l} x=2 y^{2}+4 y+5 \\ (x+1)^{2}+(y-2)^{2}=1 \end{array}\right.$$

Describe how to graph \(\frac{x^{2}}{9}-\frac{y^{2}}{1}=1\).

Describe how to locate the foci of the graph of \(\frac{x^{2}}{9}-\frac{y^{2}}{1}=1\).

The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of 4 inches and a depth of 1 inch. How far from the vertex should the light bulb be placed?

Describe one similarity and one difference between the graphs of \(\frac{x^{2}}{9}-\frac{y^{2}}{1}=1\) and \(\frac{y^{2}}{9}-\frac{x^{2}}{1}=1\).

The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of 8 inches and a depth of 1 inch. How far from the vertex should the light bulb be placed?