91Ó°ÊÓ

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$y^{2}-6 x=0$$

Write the appropriate rotation formulas so that in a rotated system the equation has no \(x^{\prime} y^{\prime}\) -term. $$10 x^{2}+24 x y+17 y^{2}-9=0$$

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 \(t\). $$x=\sqrt{t}, y=t-1 ; t \geq 0$$

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$$

Write the appropriate rotation formulas so that in a rotated system the equation has no \(x^{\prime} y^{\prime}\) -term. $$32 x^{2}-48 x y+18 y^{2}-15 x-20 y=0$$

Graph each ellipse and locate the foci. $$9 x^{2}+4 y^{2}=36$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$x^{2}-6 y=0$$

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 \(t\). $$x=\cos t, y=\sin t ; 0 \leq t < 2 \pi$$

Graph each ellipse and locate the foci. $$4 x^{2}+16 y^{2}=64$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$8 x^{2}+4 y=0$$