91Ó°ÊÓ

Graph the plane curve given by the parametric equations. Then find an equivalent rectangular equation. $$x=t^{3}+1, y=t ;-3 \leq t \leq 3$$

Use the discriminant to determine whether the graph of the equation is an ellipse (or a circle), a hyperbola, or a parabola. $$3 x^{2}-5 x y+3 y^{2}-2 x+7 y=0$$

Use the discriminant to determine whether the graph of the equation is an ellipse (or a circle), a hyperbola, or a parabola. $$5 x^{2}+6 x y-4 y^{2}+x-3 y+4=0$$

Find an equation of a parabola satisfying the given conditions. Vertex \((0,0),\) focus \((-3,0)\)

Find an equation of a parabola satisfying the given conditions. $$\text { Focus }(-\sqrt{2}, 0), \text { directrix } x=\sqrt{2}$$

Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. $$16 x^{2}+9 y^{2}=144$$

Solve. $$\begin{aligned} &3 x+y=7\\\ &4 x^{2}+5 y=56 \end{aligned}$$

Satellite Dish. \(\quad\) An engineer designs a satellite dish with a parabolic cross section. The dish is 15 ft wide at the opening, and the focus is placed 4 ft from the vertex. a) Position a coordinate system with the origin at the vertex and the \(x\) -axis on the parabola's axis of symmetry and find an equation of the parabola. b) Find the depth of the satellite dish at the vertex. (IMAGE CAN'T COPY)

Graph the cycloid. $$\begin{aligned} &x=2(t-\sin t), y=2(1-\cos t)\\\ &0 \leq t \leq 4 \pi \end{aligned}$$

Convert to radian measure. $$-315^{\circ}$$