Exam 10: Topics In Analytic Geometry

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Foci: $( \pm 10,0 )$ ; asymptotes: $y = \pm \frac { 3 } { 4 } x$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $24 x ^ { 2 } + 66 x y + 13 y ^ { 2 } = 32$

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } = 1$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 \sin ( 2 \theta )$

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10, -2), (0, -2) Asymptotes: y = ± $\frac { 4 } { 5 }$ x

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 5,1.5 )$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $y ^ { 2 } + 8 x + 5 y + 26 = 0$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 0,0 ) , ( 0,6 )$ ; major axis of length 12.

Find the center and foci of the ellipse. $\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t + 2$ $y = t ^ { 2 }$

Find the equation of the parabola with vertex at (1, 5) and focus at (-5, 5).

Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = 4 x - 2$

Select the graph for following equation. $\frac { ( x - 2 ) ^ { 2 } } { 16 } + ( y + 1 ) ^ { 2 } = 1$

Select the polar equation of graph.

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r = \cos \left( \frac { 3 \theta } { 2 } \right)$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $\left( 8 , \frac { 7 \pi } { 5 } \right)$

A simply supported beam is 12 meters long and has a load at the center (see figure). 1 $a$ Where, $a = 12 , b = 2$ The deflection of the beam at its center is 2 centimeters.Assume that the shape of the deflected beam is parabolic.Write an equation of the parabola.(Assume that the origin is at the center of the deflected beam.)

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

Use the following results the polar equation of the hyperbolla $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ is $r ^ { 2 } = \frac { - b ^ { 2 } } { 1 - e ^ { 2 } \cos ^ { 2 } \theta }$ to write the polar form of the equation of the conic $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ .