Exam 9: Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Find an equation of the form Ax² + Bx + Cy + D = 0 or Ay² + By + Cx + D = 0 for the parabola with vertex (17, 2) and focus (1, 2)

Graph the curve defined by the parametric equations. x= t , y= t² , t in [-2, 2]

Graph the equation.

The Zipper, a favorite carnival ride, maintains an elliptical shape with a major axis of 178 feet and a minor axis of 26 feet. Assuming the center of the ellipse is at (0, 14).

(a) Identify the type of conic by the discriminant, (b) transform the equation in x and y into an equation in X and Y (without an XY term) by rotating the x- and y-axes by an angle of θ to arrive at the new X- and Y-axes, and (c) graph the resulting equation (showing both sets of axes).

(a) Identify the type of conic by the discriminant, (b) transform the equation in x and y into an equation in X and Y (without an XY term) by rotating the x- and y-axes by an angle of θ to arrive at the new X- and Y-axes, and (c) graph the resulting equation (showing both sets of axes).

Graph the second-degree equation. (Hint: Transform the equation into an equation that contains no xy terms.)

Find the standard form of the equation of the hyperbola from the given graph.

Graph the ellipse.

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