91Ó°ÊÓ

Find an equation for the parabola that has a vertical axis and passes through the given points. $$P(2,5), \quad Q(-2,-3), \quad R(1,6)$$

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. $$x=-\frac{1}{3} \sqrt{9-y^{2}}$$

Find an equation for the set of points in an xy-plane such that the difference of the distances from \(F\) and \(F\) is \(k\) $$F(0,10), \quad F(0,-10) ; \quad k=16$$

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. $$x=\frac{4}{5} \sqrt{25-y^{2}}$$

Find an equation for the parabola that has a vertical axis and passes through the given points. $$P(3,-1), Q(1,-7), \quad R(-2,14)$$

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. $$r(3 \cos \theta-4 \sin \theta)=12$$

Find an equation for the set of points in an xy-plane such that the difference of the distances from \(F\) and \(F\) is \(k\) $$F(0,17), \quad F(0,-17) ; \quad k=30$$

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. $$r\left(\sin \theta+r \cos ^{2} \theta\right)=1$$

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. $$x=1+2 \sqrt{1-\frac{(y+2)^{2}}{9}}$$