91Ó°ÊÓ

Find an equation for the set of points in an xy-plane that are equidistant from the point \(P\) and the line \(l\). $$P(5,-2) ; \quad l: y=4$$

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$y^{2}=\frac{14}{3}-x^{2}$$

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. $$r^{2}\left(\cos ^{2} \theta+4 \sin ^{2} \theta\right)=16$$

Find an equation for the indicated half of the parabola. Lower half of \((y+1)^{2}=x+3\)

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. $$r^{2} \cos 2 \theta=1$$

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$x^{2}+6 x-y^{2}=7$$

Find an equation for the set of points in an \(x y\) -plane such that the sum of the distances from \(F\) and \(F^{\prime}\) Is \(k\). $$F(0,15), \quad F^{\prime}(0,-15) ; \quad k=34$$

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. $$r^{2} \sin 2 \theta=4$$

Find an equation for the indicated half of the parabola. Upper half of \((y-2)^{2}=x-4\)

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$x^{2}+4 x+4 y^{2}-24 y=-36$$