91Ó°ÊÓ

True or False The equation \(y^{2}=9+x^{2}\) is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin.

Multiple Choice If a circle rolls along a horizontal line without slipping, a fixed point \(P\) on the circle will trace out a curve called \(\mathrm{a}(\mathrm{n})\) ________. (a) cycloid (b) epitrochoid (c) hyptrochoid (d) pendulum

Find the center, vertices, and foci of each ellipse and graph it. $$x^{2}+9 y^{2}=18$$

Find an equation for the hyperbola described. Graph the equation. Vertices at (-4,0) and (4,0)\(;\) asymptote the line \(y=2 x\)

Find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. \(x^{2}-y^{2}=4\)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Focus at (-3,4)\(;\) directrix the line \(y=2\)

Find parametric equations for an object that moves along the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) with the motion described. The motion begins at \((0,3),\) is clockwise, and requires 1 second for a complete revolution.

Find an equation for the hyperbola described. Graph the equation. Center at (1,4)\(;\) focus at (-2,4)\(;\) vertex at (0,4)

Parametric equations of four plane curves are given. Graph each of them, indicating the orientation. \(\begin{array}{ll}C_{1}: & x(t)=t, \quad y(t)=\sqrt{1-t^{2}} ; \quad-1 \leq t \leq 1 \\ C_{2}: & x(t)=\sin t, \quad y(t)=\cos t ; \quad 0 \leq t \leq 2 \pi \\\ C_{3}: & x(t)=\cos t, \quad y(t)=\sin t ; \quad 0 \leq t \leq 2 \pi \\\ C_{4}: & x(t)=\sqrt{1-t^{2}}, \quad y(t)=t ; \quad-1 \leq t \leq 1\end{array}\)

Find the center, transverse axis, vertices, foci, and asymptotes, Graph each equation. \(y^{2}-x^{2}-4 y+4 x-1=0\)