91Ó°ÊÓ

Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$r=\frac{12}{6+2 \sin \theta}$$

Which polar coordinates represent the same point as \((3, \pi / 3) ?\) (a) \((3,7 \pi / 3)\) (b) \((3,-\pi / 3)\) (c) \((-3,4 \pi / 3)\) (d) \((3,-2 \pi / 3)\) (e) \((-3,-2 \pi / 3)\) (f) \((-3,-\pi / 3)\)

Exer. \(1-12\) : Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$8 y=x^{2}$$

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$$

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=t-2, \quad y=2 t+3 ; \quad 0 \leq t \leq 5$$

Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$$

Find the eccentricity, and classify the conic. Sketch the graph, and label the vertices. $$r=\frac{12}{6-2 \sin \theta}$$

Which polar coordinates represent the same point as \(-(4,-\pi / 2) ?\) (a) \((4,5 \pi / 2)\) (b) \((4,7 \pi / 2)\) (c) \((-4,-\pi / 2)\) (d) \((4,-5 \pi / 2)\) (e) \((-4,-3 \pi / 2)\) (f) \((-4, \pi / 2)\)

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=1-2 t, \quad y=1+t, \quad-1 \leq t \leq 4$$

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$\frac{y^{2}}{49}-\frac{x^{2}}{16}=1$$