91Ó°ÊÓ

Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation for the curve.

$x=3t-2,y=1-\sqrt{t},0≤t≤9$

In Problems$11-18$, find an equation of the conic described. Graph the equation by hand.

Hyperbola; center at$(0,0)$; focus at$(0,4)$; vertex at $(0,-2)$

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

$x=\sqrt{t}+4,y=\sqrt{t}-4tâ‰\yen 0$

In Problems 11–18, find an equation of the conic described. Graph the equation by hand

Ellipse; foci at $(-3,0)$and $(3,0)$; vertex at$(4,0)$

The graph of a parabola is given. Match graph to its equation.

$$\begin{gathered} A)y^2=4xC)y^2=-4xE){(y-1)}^2=4(x-1)G){(y-1)}^2=-4(x-1) \\ B)x^2=4yD)x^2=-4yF){(x+1)}^2=4(y+1)H){(x+1)}^2=4(y+1) \end{gathered}$$

In Problem, identify the graph of each equation without completing the squares.

$6x^2+3y^2-12x+6y=0$

Analyze each equation and graph it.

$r=\frac{1}{1+\cos \left(\mathrm{θ}\right)}$

Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x=3t^2,y=t+1;-∞<t<∞$

The graph of an ellipse is given. Match each graph to its equation.

$$\begin{gathered} \left(A\right)\frac{x^2}{4}+y^2=1 \\ \left(B\right)x^2+\frac{y^2}{4}=1 \\ \left(C\right)\frac{x^2}{16}+\frac{y^2}{4}=1 \\ \left(D\right)\frac{x^2}{4}+\frac{y^2}{16}=1 \end{gathered}$$

A parabolic reflector (paraboloid of revolution) is used by TV crews at football games to pick up the referee’s announcements, quarterback signals, and so on. A microphone is placed at the focus of the parabola. If a certain reflector is 4 feet wide and 1.5 feet deep, where should the microphone be placed?