91Ó°ÊÓ

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$x^{2}=12 y$$

Graph each ellipse and locate the foci. $$\frac{x^{2}}{\frac{9}{4}}+\frac{y^{2}}{\frac{25}{4}}=1$$

In Exercises \(9-20,\) use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of \(t\). $$x=t+2, y=t^{2} ;-2 \leq t \leq 2$$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: \((-4,0),(4,0) ;\) asymptote: \(y=2 x\)

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$x^{2}=8 y$$

Graph each ellipse and locate the foci. $$\frac{x^{2}}{\frac{81}{4}}+\frac{y^{2}}{\frac{25}{16}}=1$$

Write the appropriate rotation formulas so that in a rotated system the equation has no \(x^{\prime} y^{\prime}\) -term. $$5 x^{2}-8 x y+5 y^{2}-9=0$$

In Exercises \(9-20,\) use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of \(t\). $$x=t-1, y=t^{2} ;-2 \leq t \leq 2$$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Center: \((4,-2) ;\) Focus: \((7,-2) ;\) vertex: \((6,-2)\)

In Exercises \(9-20,\) use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of \(t\). $$x=t-2, y=2 t+1 ;-2 \leq t \leq 3$$