91Ó°ÊÓ

Graph the plane whose equation is given. $$ 3 x+2 z=9 $$

A reflecting telescope has a parabolic mirror that is \(20 \mathrm{ft}\) across at the top and \(4 \mathrm{ft}\) deep at the center. Where should the eyepiece be located?

Find an equation of the ellipse with foci (0,2) and (8,6) and fixed distance sum \(2 a=12\). [Hint: Here the major axis is neither horizontal nor vertical; thus none of the standard forms from this section apply. Use the definition of the ellipse.]

Graph the plane whose equation is given. $$ 3 x+z-6=0 $$

Suppose that two towers of a suspension bridge are \(350 \mathrm{ft}\) apart and the vertex of the parabolic cable is tangent to the road midway between the towers. If the cable is \(1 \mathrm{ft}\) above the road at a point \(20 \mathrm{ft}\) from the vertex, find the height of the towers above the road.

Graph the plane whose equation is given. $$ 3 x+4 y-2 z-12=0 $$

The graph of the ellipse \(x^{2} / 4+(y-1)^{2} / 9=1\) is shifted 4 units to the right. What are the center, foci, vertices, and endpoints of the minor axis for the shifted graph?

Graph the plane whose equation is given. $$ -x+2 y+z=4 $$

The graph of the ellipse \((x-1)^{2} / 9+(y-4)^{2}=1\) is shifted 5 units to the left and 3 units up. What are the center, foci, vertices, and endpoints of the minor axis for the shifted graph?

Graph the plane whose equation is given. $$ 3 x-y-6=0 $$