Deck 13: Section 1: Nonlinear Systems and the Conic Sections

Question 1

Find the distance between (-5, -4) and (-7, -3).

A)
B) 2
C)
D)

Answer 1

Question 2

Which of the following is the correct graph of ?

A)

B)

C)

D)

Answer 2

Question 3

Write the standard equation for the circle with the given radius and center. Center (-10, -2), radius 5

A) (x - 10)² + (y - 2)² = 25
B) (x - 10)² + (y - 2)² = 5
C) (x + 10)² + (y + 2)² = 5
D) (x + 10)² + (y + 2)² = 25

Answer 3

(x + 10)² + (y + 2)² = 25

Question 4

Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x² - 2x + y² + 2y - 98 = 0

A) (x + 1)² + (y - 1)² = 10; (-1, 1); 10
B) (x - 1)² + (y + 1)² = 10; (1, -1); 10
C) (x - 1)² + (y + 1)² = 100; (1, -1); 10
D) (x + 1)² + (y - 1)² = 100; (-1, 1); 10

Question 5

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 6

Determine which equation has a graph which is an ellipse.

A) 9x² - y² = 1
B)
C) x² + 9y = 1
D) x² + y² = 9

Question 7

Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. y = 5x² - 70x + 250

A) Vertex:

Focus:

Directrix:

B) Vertex:

Focus:

Directrix:

C) Vertex:

Focus:

Directrix:

D) Vertex:

Focus:

Directrix:

Question 8

Find the lengths of the legs of a right triangle whose hypotenuse is and whose area is 15 square inches.

A)
feet and
feet
B)
feet and
feet
C)
feet and
feet
D)
feet and
feet

Question 9

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 8)² - y = 1

A) Ellipse
B) Circle
C) Hyperbola
D) Parabola

Question 10

Solve the system by elimination.

A)
B)
C)
D)

Question 11

Find the midpoint and length of the line segment with the endpoints (2,3) and (5,8).

A)
B)
C)
D)

Question 12

Determine which equation has a graph which is a circle.

A) 4x² - y² = 1
B)
C) x² + 4y = 1
D) x² + y² = 4

Question 13

Solve the given system of equations. x² + y² = 625
Y = x² - 25

A) {(0, -25)}
B) {(-7, 24), (7, 24)}
C) {(0,-25), (-7, 26), (7, 26)}
D) {(0, -25), (-7, 24), (7, 24)}

Question 14

Find two complex numbers that have a sum of 12 and a product of 72.

A) 6 - 7i and 6 + 5i
B) 6 - 7i and 6 + 7i
C) 6 - 6i and 6 + 6i
D) 6 and 6

Question 15

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 16

Solve the given system of equations. y = x² - 10
5x + y = 4

A) {(2, 14), (-7, 59)}
B) {(2, -6), (-7, 39)}
C) {(2, 4), (-7, 49)}
D) {(2, -6), (-7, 49)}

Question 17

Solve the given system of equations. xy = 10
Y = x

A) Ø
B)

C) {(-10, -10), (0, 0), (10, 10)}
D) {(0, 10), (10, 0)}

Question 18

Find the equation of the parabola with the given focus and directrix. Focus: (3, 0); Directrix: y = -4

A)

B)

C)

D)

Question 19

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 20

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

A) Vertex: (6, 7); Focus: (-6, 5); Directrix: y = 5
B) Vertex: (6, 7); Focus: (-6, 9); Directrix: y = 9
C) Vertex: (-6, 7); Focus: (-6, 9); Directrix: y = 5
D) Vertex: (-6, 7); Focus: (-6, 5); Directrix: y = 9

Question 21

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = x² - 4
X² + 4y² = 4

A) (0, -1), (-2, 0), (2, 0)

B) (0, 1), (-2, 0), (2, 0)

C) (-2, 0), (2, 0)

D) (-2, 0), (2, 0)

Question 22

Which of the following graphs correctly represents the solution set for the given system of inequalities?

A)

B)

C)

D)

Question 23

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 24

Determine which equation has a graph which is a hyperbola.

A) 9x² - y² = 1
B) x² + 9y = 1
C) x² + y² = 9
D)

Question 25

Determine which equation has a graph which is a parabola.

A) x² + 16y = 1
B)
C) x² + y² = 16
D) 16x² - y² = 1