Exam 9: Conic Sections Systems of Non-Linear Equations

The radius of the outer edge of a semi-circular window is 6 in. Write an equation that is a model of this window. Assume the origin is at the lower left corner of the window.

The center of an ellipse is (4, -2) . The major axis is vertical, and the distance between the vertices on the major axis is 18. The minor axis is horizontal, and the distance between the vertices on the minor axis is 10. Identify the vertices.

Solve the system of equations by elimination. -

Use the equation -Identify the vertices of the minor axis.

Write the equation of the parabola with the given vertex, point on the parabola, and axis of symmetry. -Vertex ; point ;

Solve the system of equations by substitution. -

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) . -For the hyperbola write the equations of the asymptotes.

The two legs of a right triangle measure 6 in. and 7 in. Find the exact length of the hypotenuse. Do not round.

Use the parabola to answer the questions. -Write the equation of the directrix.

Solve the system of equations by substitution. -

Solve the system of equations by substitution. -

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) . -The foci of a hyperbola are and , and the vertices are And . Identify a, b, and p.

Use the parabola to answer the questions. -Write the equation of the axis of symmetry.

Find the midpoint of the line segment with the endpoints (-9 ,3) and (8, -5) .

Write the equation in standard form of the circle with center and passing through the point

Write the equation of the parabola with the given vertex, point on the parabola, and axis of symmetry. -Vertex ; point ;

Use the equation -Rewrite the equation of the ellipse in standard form.

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) . The foci of a hyperbola are (-9, 0) and (9, 0) , and the vertex is ( -6, 0) . -Write the equation of the hyperbola.

The major axis of an ellipse is horizontal, and the vertices of the major axis are and . The minor axis is vertical, and the vertices of the minor axis are and . Write the equation in standard form.

Graph the system of equations, and use the graph to estimate the solutions. -