Exam 13: Section 2: Nonlinear Systems and the Conic Sections

Graph .

Solve the given system of equations. x² + y² = 25 y = x² - 5

Find the midpoint and length of the line segment with the endpoints (5,9) and (8,14).

Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x² - 18x + y² + 6y - 10 = 0

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 5)² + y² = 1

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = 1 - x² x² + 4y² = 4

Pump A can either fill or empty a tank in the same amount of time. If pump A and pump B are working together, the tank can be filled in 36 minutes. When pump A is draining the tank while pump B is filling it, the tank fills in 180 minutes. How long would it take either pump working alone to fill the tank?

Graph .

Solve the system by elimination. Show your work.

Which, if any, of the ordered pairs (3, 4), (-1, 7), (-3, -1), and (8, -5) satisfy the system of inequalities? x² + y² ≤ 25 y < x²

Write the standard equation for the circle with the given radius and center. Center (8, -5), radius 12

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 1)² - y = 1

Find the vertex, focus, and directrix for the given parabola.

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 9)² + 3y² = 1

Graph .

Graph the solution set for the given system of inequalities.

Graph .

Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. y = 6x² + 36x + 55

Find two complex numbers that have a sum of -14 and a product of 58.

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 9)² - y² = 1