Exam 10: Topics in Analytic Geometry

In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 400 m apart, and the lowest point of the suspension cables is 100 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the lowest point of the cable. NOTE: This equation is used to find the length of the cable needed in the construction of the bridge.

Find the vertices and asymptotes of the hyperbola.

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 4).

Graph the hyperbola.

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

Find the vertices and asymptotes of the hyperbola.

A solar oven uses a parabolic reflector to focus the sun's rays at a point 8 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 8 inches

Give the coordinates of the circle's center and its radius.

Find the center and vertices of the hyperbola.

Find the center and vertices of the ellipse.

Find the vertices and asymptotes of the hyperbola.

Give the coordinates of the circle's center and its radius.

Identify the graph of the following ellipse.

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Give the coordinates of the circle's center and its radius.

Find the center and foci of the ellipse.

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0, -2), (6, -2) Asymptotes: