91Ó°ÊÓ

Find an equation for the set of points in an xy-plane that are equidistant from the point \(P\) and the line \(l\). $$P(7,0) ; \quad l: x=1$$

Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix. $$e=\frac{3}{4}, \quad r \sin \theta=5$$

Show that \(x=a \sec t+h, \quad y=b \tan t+k\) $$-\pi / 2

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 \(k\). $$F(3,0), \quad F^{\prime}(-3,0) ; \quad k=10$$

Find an equation for the set of points in an xy-plane that are equidistant from the point \(P\) and the line \(l\). $$P(-6,3) ; \quad l: x=-2$$

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$\frac{1}{3}(x+2)=y^{2}$$

Find a polar equation of the parabola with focus at the pole and the given vertex. $$v\left(4, \frac{\pi}{2}\right)$$

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. $$r^{2}\left(4 \sin ^{2} \theta-9 \cos ^{2} \theta\right)=36$$

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 \(k\). $$F(12,0), \quad F^{\prime}(-12,0) ; \quad k=26$$

(a) Find three parametrizations that give the same graph as the given equation. (b) Find three parametrizations that give only a portion of the graph of the given equation. $$y=\ln x$$