91Ó°ÊÓ

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph. \(9 x^{2}-16 y^{2}=1\)

15–22 (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices. $$r=\frac{8}{3+3 \cos \theta}$$

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$x-7 y^{2}=0$$

\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} $$ x=\cos 2 t, \quad y=\sin 2 t $$

(a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the \(x y\) -term. (c) Sketch the graph. $$13 x^{2}+6 \sqrt{3} x y+7 y^{2}=16$$

\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} $$ x=\sec t, \quad y=\tan t, \quad 0 \leq t<\pi / 2 $$

15–22 (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices. $$r=\frac{2}{1-\cos \theta}$$

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$5 x+3 y^{2}=0$$

(a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the \(x y\) -term. (c) Sketch the graph. $$x^{2}+2 \sqrt{3} x y-y^{2}+2=0$$

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$8 x^{2}+12 y=0$$