91Ó°ÊÓ

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph. \(9 x^{2}-4 y^{2}=36\)

Find the center, foci, vertices, and asymptotes of the hyperbola. Then sketch the graph. $$ (x-8)^{2}-(y+6)^{2}=1 $$

\begin{array}{l}{1-22 \text { a pair of parametric equations is given. }} \\\ {\text { (a) Sketch the curve represented by the parametric equations. }} \\\ {\text { (b) Find a rectangular-coordinate equation for the curve by }} \\\ {\text { eliminating the parameter. }}\end{array} $$ x=|t|, \quad y=|1-| t| | $$

\begin{array}{l}{1-22 \text { a pair of parametric equations is given. }} \\\ {\text { (a) Sketch the curve represented by the parametric equations. }} \\\ {\text { (b) Find a rectangular-coordinate equation for the curve by }} \\\ {\text { eliminating the parameter. }}\end{array} $$ x=2 \sin t, \quad y=2 \cos t, \quad 0 \leq t \leq \pi $$

Find the center, foci, vertices, and asymptotes of the hyperbola. Then sketch the graph. $$ y^{2}-\frac{(x+1)^{2}}{4}=1 $$

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph. \(25 y^{2}-9 x^{2}=225\)

Find the vertices, foci, and eccentricity of the ellipse. Determine the lengths of the major and minor axes, and sketch the graph. $$ 2 x^{2}+y^{2}=3 $$

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$y=5 x^{2}$$

Determine the equation of the given conic in \(X Y\) -coordinates when the coordinate axes are rotated through the indicated angle. $$x^{2}+2 \sqrt{3} x y-y^{2}=4, \quad \phi=30^{\circ}$$

Find the center, foci, vertices, and asymptotes of the hyperbola. Then sketch the graph. $$ \frac{(y-1)^{2}}{25}-(x+3)^{2}=1 $$