91Ó°ÊÓ

Find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility.

$x^2-3y^2+8x-6y+4=0$

In Problem 62, we graphed the hypocycloid. Now graph the rectangular equations of the hypocycloid. Did you obtain a complete graph? If not, experiment until you do.

Find an equation for each ellipse. Graph the equation by hand.

Center at$(1,2)$: vertex at$(4,2)$:contains the point$(1,5)$

Satellite Dish- A satellite dish is shaped like a paraboloid

of revolution. The signals that emanate from a satellite strike

the surface of the dish and are reflected to a single point,

where the receiver is located. If the dish is 10 feet across at

its opening and 4 feet deep at its center, at what position

should the receiver be placed?

Graph each function by hand. Be sure to label any intercepts.

$f\left(x\right)=\sqrt{16+4x^2}$

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at

its opening and 4 feet deep at its center, at what position should the receiver be placed?

Find an equation for each ellipse. Graph the equation by hand.

Center at$(1,2)$vertex at$(1,4)$ contains the point$(1+\sqrt{3},3)$.

Constructing a TV Dish - A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.

Graph each function by hand. Be sure to label any intercepts.

$f\left(x\right)=-\sqrt{9+9x^2}$

Look up the curves called hypocycloid and epicycloid. Write a report on what you find. Be sure to draw comparisons with the cycloid.