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

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

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

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

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

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 18x² - 20x - 13y² + 15y + 10 = -8

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

If the xy-coordinate axes are rotated 30°, find the XY coordinates of the point (x, y) = .

(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 each equation and find the point(s) of intersection. X² + y² = 1 -x + y = 7

The difference of two numbers is 74 and the difference of their squares is 3700. Find the numbers.

Graph the parabola and label the coordinates of the vertex.

Find the standard form of the ellipse with the following equation. 36x² + 4y² - 144x - 24y = -36

Identify the conic that the polar equation represents.

Find the standard form of the hyperbola with the following equation. 7x² - 3y² - 112x - 30y = -352

If the xy-coordinate axes are rotated 30°, find the XY coordinates of the point (x, y) = .

Solve the system of equations by applying the elimination method. 9x² + 5y = 4 -9x² - 5y = 4

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, 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 465 ft/sec at an angle of 33° with the horizontal. How far does the projectile travel (what is the horizontal distance), and what is the maximum altitude? Round to the nearest integer.

Find the standard form of the equation of an ellipse with foci (2, 0) and (-2, 0), and vertices (6, 0) and (-6, 0).

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