91Ó°ÊÓ

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}=-8 x $$

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 \(t.\) \(x=\left(60 \cos 30^{\circ}\right) t, y=5+\left(60 \sin 30^{\circ}\right) t-16 t^{2} ; t=2\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$ \frac{x^{2}}{49}+\frac{y^{2}}{81}=1 $$

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

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 \(t.\) \(x=\left(80 \cos 45^{\circ}\right) t, y=6+\left(80 \sin 45^{\circ}\right) t-16 t^{2} ; t=2\)

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}=-12 x $$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$ \frac{x^{2}}{64}+\frac{y^{2}}{100}=1 $$

find the standard form of the equation of each hyperbola satisfying the given conditions. $$\text { Foci: }(-7,0),(7,0) ; \text { vertices: }(-5,0),(5,0)$$

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

find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: \((0,-6),(0,6) ;\) asymptote: \(y=2 x\)