Exam 10: The Conic Sections

Solve the problem. Round to the nearest tenth when necessary. -The roof of a building is in the shape of the hyperbola where x and y are in meters. Determine the distance, w, between the outside walls. A = 9 m

Use the value of AC to identify the conic. -

Find the foci and asymptotes of the hyperbola. -

Graph the conic. -r

Find the eccentricity and use it to identify the conic as a parabola, ellipse, or hyperbola. -

Provide an appropriate response. -Explain why the graph of an ellipse does not satisfy the conditions for the graph of a function.

Write the equation for the circle described. -Endpoints of a diameter with coordinates (1, -5) and (8, 1)

Write the polar equation for a conic with focus at the origin and the given eccentricity and directrix. -e = 1, x = 2

Write an equation for the ellipse. -Foci and x-intercepts

Find the new coordinates of the given point when the xy-coordinate system is rotated by the indicated angle. -(3, -8); 60°

Write an equation in the x'y'-system for the graph of the given equation in the xy-system using the given angle of rotation. -

Find the eccentricity and use it to identify the conic as a parabola, ellipse, or hyperbola. -

Graph the parabola. -

Find the vertex of the parabola, and determine whether the parabola opens upward, downward, to the left, or to the right. -

Graph the parabola. -

Use rotation of axes to eliminate the product term. -

Find the equation of the hyperbola. -Vertices at (8, 0) and (-8, 0), foci at (11, 0) and (-11, 0)

Provide an appropriate response. -It can be shown that an ellipse with foci (c, 0) and (-c, 0), where the sum of the distances from any point (x, y) of the ellipse to the two foci is 2a, has the equation . Use this result to find an equation of an Ellipse with foci (3, 0) and (-3, 0), where the sum of the distances from any point of the ellipse to the two foci is 12.