Use the discriminant to determine whether the graph of the following equation is a parabola, an ellipse, or a hyperbola. 6x2 + 4xy + 3y2 = 42 parabola ellipse hyperbola Use rotation of axes to eliminate the xy-term in the equation. (Enter your answer in terms of the xy-coordinate system.) Sketch a graph of the equation. y 10 F 5 * -10 -5 5 10 -5 -10 __ y) = -10 -5 y 10 -5 -10 5 (larger x-value) -X 10 -10 Find the coordinates of the vertices of this conic (in the xy-coordinate system). - y) = (smaller x-value) -10 -5 -5 y 10 5 -5 -10 y 10 5 -5 -10 5 10 10 X X

Find the standard form of the equation of the parabola shown in the figure below.

Find the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.

The light bulb in a flashlight is at the focus of the parabolic reflector, 1.5 centimeters from the vertex of the reflector (see figure). Write an equation for a cross section of the flashlight’s reflector with its focus on the positive x-axis and its vertex at the origin.

?Write the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.