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

Question 1

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

Answer 1

{(0, -5), (-3, 4), (3, 4)}

Question 2

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

Answer 2

Hyperbola

Question 3

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

Answer 3

Vertex: (1, -5); Focus: (1, -2);
Directrix: y = -8

Question 4

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

Question 5

Graph .

Question 6

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

Question 7

Graph .

Question 8

Solve the given system of equations.
y = x² + 4
-7x + y = -6

Question 9

Solve the given system of equations.
xy = 3
y = x

Question 10

Find the distance between (-10, 1) and (-12, 2).

Question 11

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

Question 12

Graph .

Question 13

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?

Question 14

Find the center and radius for the given circle.
169 - x² = (y - 4)²

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

Solve the system by elimination. Show your work.

Question 20

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

Question 21

Graph .

Question 22

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

Question 23

Graph the solution set for the given system of inequalities.

Question 24

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