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

Find the standard form of the equation of the hyperbola with foci (-9, 0) and (9, 0), and vertices (-1, 0) and (1, 0).

Find the standard form of the equation of the hyperbola with foci (-8, 0) and (8, 0), and vertices (-6, 0) and (6, 0).

Graph the nonlinear inequality.

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

Find the equation of the ellipse with the given graph.

Solve the system of equations by applying the substitution method.

Find the standard form of the equation of an ellipse with foci (0, -5) and (0, 5) and vertices (0, -7) and (0, 7).

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

Solve the system of equations by applying the elimination method.

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

Match the ellipse to the equation.

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

Solve the system of equations by applying the substitution method. X² + y² = 13 X - y = -5

Find the general equation of the hyperbola from the given graph.

Find an equation for the parabola with vertex (3, 10) and focus (5, 10).

Find the standard form of the ellipse with the following equation. 25x² + 9y² + 50x + 90y = -25

Graph the ellipse.

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 baseball is hit at an initial speed of 110 mph and angle of 24° at a height of 5 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.

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 gun is fired at an angle of 23°, and the bullet has an initial speed of 2345 feet per second. How high does the bullet go, and when does it hit the ground? Round the altitude to the nearest foot and time to the nearest tenth of a second.

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