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Magazine Problem 15
Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$8 x^{2}+4 y=0$$
Problem 16
Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$8 y^{2}+4 x=0$$
Problem 16
Graph each ellipse and locate the foci. $$4 x^{2}+25 y^{2}=100$$
Problem 16
Write the appropriate rotation formulas so that in a rotated system the equation has no \(x^{\prime} y^{\prime}\) -term. $$3 x y-4 y^{2}+18=0$$
Problem 16
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 \(t\). $$x=-\sin t, y=-\cos t ; 0 \leq t < 2 \pi$$
Problem 16
Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{x^{2}}{144}-\frac{y^{2}}{81}=1$$
Problem 17
Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((7,0) ;\) Directrix: \(\quad x=-7\)
Problem 17
Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{y^{2}}{16}-\frac{x^{2}}{36}=1$$
Problem 17
Write the appropriate rotation formulas so that in a rotated system the equation has no \(x^{\prime} y^{\prime}\) -term. $$34 x^{2}-24 x y+41 y^{2}-25=0$$
Problem 17
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 \(t\). $$x=t^{2}, y=t^{3} ;-\infty < t < \infty$$
