91Ó°ÊÓ

Find an equation for the set of points in an xy-plane such that the difference of the distances from \(F\) and \(F\) is \(k\) $$F(13,0), \quad F(-13,0) ; \quad k=24$$

Determine whether the graph of the equation is the upper, lower, left, or right half of a parabola, and find an equation for the parabola. $$x=-\sqrt{y+7}-3$$

Exer. \(51-58:\) Determine whether the graph of the equation is the upper, lower, left, or right half of an ellipse, and find an equation for the ellipse. $$y=11 \sqrt{1-\frac{x^{2}}{49}}$$

Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. Use it to help sketch the graph in an \(r \theta\) -plane. $$r^{2} \cos 2 \theta=1$$

Graph the Lissajous figure in the viewing rectangle \([-1,1]\) by \([-1,1]\) for the specified range of \(t\). $$x(t)=\sin (4 t), \quad y(t)=\sin (3 t+\pi / 6) ; \quad 0 \leq t \leq 6.5$$

Determine whether the graph of the equation is the upper, lower, left, or right half of a parabola, and find an equation for the parabola. $$x=\sqrt{y-4}+8$$

Exer. \(51-58:\) Determine whether the graph of the equation is the upper, lower, left, or right half of an ellipse, and find an equation for the ellipse. $$y=-6 \sqrt{1-\frac{x^{2}}{25}}$$

Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. Use it to help sketch the graph in an \(r \theta\) -plane. $$r^{2} \cos 2 \theta=-9$$

Find an equation for the set of points in an xy-plane such that the difference of the distances from \(F\) and \(F\) is \(k\) $$F(5,0), \quad F(-5,0) ; \quad k=8$$

Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. Use it to help sketch the graph in an \(r \theta\) -plane. $$r(\sin \theta-2 \cos \theta)=6$$