91Ó°ÊÓ

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

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

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$4 x^{2}-16 x+9 y^{2}+36 y=-16$$

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. $$r\left(r \sin ^{2} \theta-\cos \theta\right)=3$$

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

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

Shown in the figure is the Lissajous figure given by $$x=2 \sin 3 t, \quad y=3 \sin 1.5 t ; \quad t \geq 0$$ Find the period of the figure - that is, the length of the smallest \(t\) -interval that traces the curve. (GRAPH CAN'T COPY)

Find an equation for the parabola that has a horizontal axis and passes through the given points. $$P(-1,1), \quad Q(11,-2), \quad R(5,-1)$$

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola. $$x^{2}+3 x=3 y-6$$