91Ó°ÊÓ

Rotate the coordinate axes to remove the \(xy-term.\) Then identify the type of conic and sketch its graph. $$x y=-9$$

Sketch the parabola, and label the focus, vertex, and directrix. $$ \text { (a) } y^{2}=4 x \quad \text { (b) } x^{2}=-8 y $$

Sketch the curve by eliminating the parameter, and indicate the direction of increasing \(t .\) $$ x=3 t-4, y=6 t+2 $$

Sketch the parabola, and label the focus, vertex, and directrix. $$ \text { (a) } y^{2}=-10 x \quad \text { (b) } x^{2}=4 y $$

Sketch the curve by eliminating the parameter, and indicate the direction of increasing \(t .\) $$ x=t-3, y=3 t-7 \quad(0 \leq t \leq 3) $$

Find the slope of the tangent line to the polar curve for the given value of \(\theta\) $$ r=a \sec 2 \theta ; \quad \theta=\pi / 6 $$

Rotate the coordinate axes to remove the \(xy-term.\) Then identify the type of conic and sketch its graph. $$x^{2}-x y+y^{2}-2=0$$

Find the rectangular coordinates of the points whose polar coordinates are given. $$ \begin{array}{llll}{\text { (a) }(-2, \pi / 4)} & {\text { (b) }(6,-\pi / 4)} & {\text { (c) }(4,9 \pi / 4)} & {}\end{array} $$ $$ \begin{array}{llll}{\text { (d) }(3,0)} & {\text { (e) }(-4,-3 \pi / 2)} & {\text { (f) }(0,3 \pi)} & {}\end{array} $$

Rotate the coordinate axes to remove the \(xy-term.\) Then identify the type of conic and sketch its graph. $$x^{2}+4 x y-2 y^{2}-6=0$$

Sketch the curve by eliminating the parameter, and indicate the direction of increasing \(t .\) $$ x=2 \cos t, y=5 \sin t \quad(0 \leq t \leq 2 \pi) $$