Exam 8: Conics and Systems of Nonlinear Equations and Inequalities

Find an equation of the form for the parabola with vertex (-1, 6) and focus (5, 6).

Graph the equation.

Find the standard form of the equation of an ellipse with vertices (-6, 0) and (6, 0) and minor axis (0, -5) and (0, 5).

Find the equation of the hyperbola from the given graph.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

Solve the system of equations by applying the elimination method.

Identify the conic section as a parabola, circle, ellipse, or hyperbola:The set of all points equidistant from the point (-11, -4) and the line

Find the length of the latus rectum of the parabola with equation = 20( y - 4).

Identify the conic section as a parabola, ellipse, circle, or hyperbola:The set of all points whose distance from the point (4, 9) plus the distance from the point is exactly 39 units.

Find the standard form of the equation of the hyperbola with foci (-10, 0) and and vertices (-2, 0) and (2, 0).

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

Find the standard form of the equation of a hyperbola with center (0, 0), transverse x-axis, and asymptotes y = 11x and

Find the equation of the directrix of the parabola with equation = 12( y - 5).

Solve the system of equations by applying the substitution method.

A bridge with a parabolic shape has an opening 98 feet wide at the base of the bridge (where the bridge meets the water), and the height in the center of the bridge is 40 feet. A sailboat whose mast reaches 50 feet above the water is traveling under the bridge 23 feet from the center of the bridge. Will it clear the bridge without scraping its mast? Justify your answer.

Identify the conic section as a parabola, ellipse, circle, or hyperbola:The set of all points equidistant from the point (8, 2) and the line y = -4.

Match the equation to the parabola.

Find the standard form of the equation of the ellipse with the given graph.

A satellite dish measures 72 feet across its opening and 9 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.