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

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

Graph the curve defined by the parametric equations. , ,t in [0, 2π]

Match the ellipse to the equation.

Graph the curve defined by the parametric equations. , ,t in [0, 2π]

Graph each equation and find the point(s) of intersection. x² + y = 35 x² - y = -35

If the xy-coordinate axes are rotated 60°, find the XY coordinates of the point (x, y) = .

Recall that the flight of a projectile can be modeled with the parametric equations: , where t is in seconds, v_o is the initial velocity, $\theta$ is the angle with the horizontal, and x and y are in feet. A missile is fired from a ship at an angle of 31°, an initial height of 13 feet above the water's surface, and at a speed of 5500 feet per second. How long will it be before the missile hits the water? Round to one decimal place.

Graph each equation and find the point(s) of intersection. X² + y = 3 X² - y = -3

Identify the conic that the polar equation represents.

Graph the ellipse.

Graph the curve defined by the parametric equations. , ,t in [-π/4,π/4]

Graph the system of inequalities.

Graph the curve defined by the parametric equations.

Match the parabola to an equation in standard form.

A family moves into a new home and decides to fence in the yard to give its dog room to roam. If the area that will be fenced in is rectangular and has an area of 18,723 square feet, and the length is three times as much as the width, how many linear feet of fence should they buy?

For the polar equation, (a) Identify the conic as either a parabola, ellipse, or hyperbola; (b) find the eccentricity and vertex (or vertices); and (c) graph.

For the polar equation, graph the conic.

Match the parabola to the equation.

The given parametric equations define a plane curve. Find an equation in rectangular form that also corresponds to the plane curve. ,

(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).