91Ó°ÊÓ

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}=4 x $$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((0,20) ;\) Directrix: \(y=-20\)

Find the standard form of the equation of each ellipse satisfying the given conditions. Foci: \((-2,0),(2,0) ; y\) -intercepts: \(-3\) and 3

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$(x+3)^{2}-9(y-4)^{2}=9$$

Graph each ellipse and give the location of its foci. $$\frac{x^{2}}{25}+\frac{(y-2)^{2}}{36}=1$$

A satellite dish, like the one shown at the top of the next column, is in the shape of a parabolic surface. Signals coming from a satellite strike the surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish shown has a diameter of 12 feet and a depth of 2 feet. How far from the base of the dish should the receiver be placed?

Explain how to use \(y^{2}=8 x\) to find the parabola's focus and directrix.

Which one of the following is true? a. If one branch of a hyperbola is removed from a graph, then the branch that remains must define \(y\) as a function of \(x .\) b. All points on the asymptotes of a hyperbola also satisfy the hyperbola's equation. c. The graph of \(\frac{x^{2}}{9}-\frac{y^{2}}{4}=1\) does not intersect the line \(y=-\frac{2}{3} x\) d. Two different hyperbolas can never share the same asymptotes.

Find the equation of a hyperbola whose asymptotes are perpendicular.