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

Find the standard form of the equation of the ellipse with the given graph.

Find an equation for the parabola with vertex (-1, -5) and focus (5, -5).

A conic section that is a set of all points equidistant from a point, is called a

Solve the system of equations by applying the substitution method. X² - y² = 0 Xy = -25

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

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 projectile is launched at a speed of 420 ft/sec at an angle of 37° with the horizontal. After how many seconds does the projectile hit the ground? Round to one decimal place.

Identify the conic (parabola, ellipse, or hyperbola) that is represented by the equation.

(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).

Recall that the flight of a projectile can be modeled with the parametric equations: , where t is in seconds, ν_o is the initial velocity, θ is the angle with the horizontal, and x and y are in feet. A baseball is hit at an initial speed of 110 mph and angle of 31° at a height of 2 feet above the ground. If there's no back fence or other obstruction, how far does the baseball travel (horizontal distance), and what is the maximum height? Round to one decimal place.

Match the equation to the parabola.

Solve the system of equations by applying the substitution method. X² + y² = 73 Xy = 24

For the polar equation, graph the conic.

Find the equation of the hyperbola from the given graph.

For the polar equation, graph the conic.

Identify the conic that the polar equation represents.

Graph the hyperbola.

The given rectangular equation defines a plane curve. Find the parametric equations that also corresponds to the plane curve.

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

Graph the curve defined by the parametric equations.

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