91Ó°ÊÓ

If the center of an ellipse is $(2,-3)$, the major axis is parallel to the x-axis, and the distance from the center of the ellipse to its vertices is $a=4units$, then the coordinates of the vertices are _____ and _____.

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

Parabola; focus at $\left(-2,0\right)$; directrix the line$x=2$

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.

$x=t^2+4,y=t^2-4;-∞<t<∞.$

Identify the conic that each polar equation represents. Also, give the position of the directrix

$r=\frac{6}{8+2\sin \left(\mathrm{θ}\right)}$

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

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

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

and equations are,

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

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.

$x=\sqrt{t}+4,y=\sqrt{t}-4;tâ‰\yen 0$

If the foci of an ellipse are $(-4,4)and(6,4)$, then the coordinates of the center of the ellipse are _____ .

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

$x=3t-2,y=1-\sqrt{t},0≤t≤9$

Find the rectangular equation of the curve.

$x=5\tan t,y=se{c}^{2}t,-\frac{\mathrm{Ï€}}{2}<t<\frac{\mathrm{Ï€}}{2}$