Exam 9: Analytic Geometry

Graph the equation. - $y^{2}=16 x$ A) B) C) D)

Graph the curve whose parametric equations are given. - $\mathrm{x}=\mathrm{t}+2, \mathrm{y}=3 \mathrm{t}-1 ; 0 \leq \mathrm{t} \leq 3$ A) B) C) D)

Find a rectangular equation for the plane curve defined by the parametric equations. - $\mathrm { x } = 3 \mathrm { t } , \mathrm { y } = \mathrm { t } + 1 ; - 2 \leq \mathrm { t } \leq 3$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 9 } { 3 + 3 \sin \theta }$

Find the center, foci, and vertices of the ellipse. - $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - $24 x y - 7 y ^ { 2 } + 36 = 0$

Find parametric equations for the rectangular equation. - $y = x ^ { 4 } - 4$

Find an equation for the ellipse described. Graph the equation. -Center at $( - 2,3 ) ;$ focus at $( - 7,3 ) ;$ contains the point $( - 8,3 )$

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $x y+16=0$

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center? A) $\frac { 121 } { 1984 }$ in. B) $\frac { 363 } { 496 }$ in. C) $\frac { 961 } { 132 }$ in. D) $\frac { 1089 } { 124 } \mathrm { in }$ .

Find an equation of the parabola described. -Focus at (-3, 0); directrix the line x = 3 A) $y ^ { 2 } = - 12 x$ B) $x ^ { 2 } = - 12 y$ C) $y ^ { 2 } = - 3 x$ D) $y ^ { 2 } = 12 x$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $(x-3)^{2}=(y-3)$ A) vertex: (3,3) focus: (3,3.25) directrix: y=2.75 B) vertex: (-3,-3) focus: (-2.75,-3) directrix: x=-3.25 C) vertex: (3,3) focus: (3.25,3) directrix: x=2.75 D) vertex: $(-3,-3)$ focus: $(-3,-2.75)$ directrix: $y=-3.25$

Graph the hyperbola. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 49$ , where $x$ and $y$ are in meters. Determine the distance, $w$ , the outside walls are apart, if the height of each wall is $12 \mathrm {~m}$ .

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( x + 1 ) ^ { 2 } = 12 ( y - 4 )$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - $5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0$

Graph the curve whose parametric equations are given. - $x = 3 \cos t , y = - 3 \sin t ; \frac { \pi } { 2 } \leq t \leq \frac { 3 \pi } { 2 }$