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

Find an equation for the parabola with focus (0, 5) and directrix x = 2.

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 gun is fired at an angle of 21°, and the bullet has an initial speed of 875 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.

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 projectile is launched at a speed of 560 ft/sec at an angle of 47° with the horizontal. After how many seconds does the projectile hit the ground? Round to one decimal place.

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

Write an equation for the parabola in general form.

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 missile is fired from a ship at an angle of 32°, an initial height of 20 feet above the water's surface, and at a speed of 4450 feet per second. How long will it be before the missile hits the water? Round to the nearest tenth of a second.

Graph the hyperbola.

For the polar equation, graph the conic.

Solve the system of equations by applying the elimination method. X² - 10y = -16 2x - 5y = -6

Match the graph to the nonlinear inequality.

Find the polar equation that represents the conic described (assume the focus is at the origin). Parabola with eccentricity e =1 and directrix

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 48x² - 16y² = 6

If the xy-coordinate axes are rotated 45°, find the XY coordinates of the point (x, y) = (3, -6).

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.

Match the equation to the parabola.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. X² - 2x + y² + 10y + 5 = 10

Find the equation of the ellipse with the following properties: major axis horizontal with length of 168, minor axis length of 30 and centered at (-3, 9).

Find the standard form of the ellipse with the following equation. 1x² + 9y² + 8x + 90y = -232

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