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 vertex and directrix of the parabola.

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: foci:

Find the vertex and focus of the parabola.

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 hyperbola with the given characteristics. vertices: (-6, -2), (-2, -2) Asymptotes:

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-2, 1), (6, 1) Asymptotes:

Identify the conic by writing the equation in standard form.

Identify the conic by writing the equation in standard form.

Graph the hyperbola.

Find the center and vertices of the ellipse.

Graph the hyperbola.

Write the equation of the ellipse with foci at (2, 4), (6, 4), and b = 2.

Find the vertices and asymptotes of the hyperbola.

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

Identify the graph of the following ellipse.

Find the vertices and asymptotes of the hyperbola.

Graph the following equation.

Identify the conic by writing the equation in standard form.