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

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

Write an equation for the parabola.

Match the graph to the nonlinear inequality.

Graph the ellipse.

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

Find an equation for the parabola with vertex (10, -2) and focus (10, 4).

Graph each equation and find the point(s) of intersection. X² + y² = 26 Y = 5

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

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.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 4x² - 2x + 13y² - 12y + 20 = 2

Graph the hyperbola.

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

Write an equation for the parabola in standard form.

Find an equation for the parabola with focus (9, 3) and directrix y = 9.

Find an equation for the parabola with vertex (2, 10) and focus (10, 10).

Graph the curve defined by the parametric equations. , ,t in [0, 1]

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

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.

Graph the curve defined by the parametric equations.

A satellite dish measures 30 feet across its opening and 13 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?