91Ó°ÊÓ

Find the standard form of the equation of each hyperbola satisfying the given conditions. $$\text { Foci: }(0,-3),(0,3) ; \text { vertices: }(0,-1),(0,1)$$

a. Identify the conic section that each polar equation represents. b. Describe the location of a directrix from the focus located at the pole. $$r=\frac{8}{2+2 \sin \theta}$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$y^{2}=16 x$$

Write each equation in terms of a rotated \(x^{\prime} y^{\prime}-\) system using \(\theta,\) the angle of rotation. Write the equation involving \(x^{\prime}\) and \(y^{\prime}\) in standard form. $$13 x^{2}-6 \sqrt{3} x y+7 y^{2}-16=0 ; \theta=60^{\circ}$$

Find the standard form of the equation of each hyperbola satisfying the given conditions. $$\text { Foci: }(0,-6),(0,6) ; \text { vertices: }(0,-2),(0,2)$$

Graph each ellipse and locate the foci. $$\frac{x^{2}}{49}+\frac{y^{2}}{36}=1$$

In Exercises \(1-8,\) parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of \(t\). $$x=2+3 \cos t, y=4+2 \sin t ; t=\pi$$

a. Identify the conic section that each polar equation represents. b. Describe the location of a directrix from the focus located at the pole. $$r=\frac{8}{2-2 \sin \theta}$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$y^{2}=4 x$$

a. Identify the conic section that each polar equation represents. b. Describe the location of a directrix from the focus located at the pole. $$r=\frac{12}{2-4 \cos \theta}$$