Take the Algebra 2 Chapter 14 Test.
If the vertex is (1, 2) and the directrix is y = 7, what is the focus?
(1, -3)
Solve the system algebraically.
(2, 10) (-2, -10)
Write the standard-form equation of the circle that has a diameter with endpoints (-44, -7) and (4, 7).
(x + 20)2 + y2 = 625
Which of the following equations could represent the graph?
(x + 3)2 + (y + 3)2 = 9
Which of the following equations could represent the graph? two lines one above x axis one below x axis
(y - 2)^2/4 - (x - 2)^2/64 = 1
What are the numbers of possible solutions to a system of an ellipse and a hyperbola if they have the same center? Select all that apply.
0, 2
Two different circles can intersect in a maximum of _____ points.
2
Which of the following are equations of a circle? Select all that apply.
2x2 + 2y2 - 3x = 9; x2 + y2 + 4x - 6y = 12
Which of the following are equations of ellipses? Select all that apply.
3(x + 2)^2 + (y + 1)^2 = 5; (x - 3)^2 = 7 - 4(y + 2)^2; 4x^2 + 8x +8y^2 + 12y = 5
State the center and radius of (x - 7)2 + (y + 3)2 = 9.
C(7, -3), r = 3
The major axis of the ellipse is horizontally stretched.
False
Describe how the graph of the equation changes when a = b.
The ellipse turns into a circle.
A system involving two different conic equations can have at most four solutions.
True
Identify the conic represented by x2 + 8x + y2 - 6y - 11 = 0.
circle
The plane is perpendicular to the axis and does not contain the vertex.
circle
Which of the following ellipses has the smallest eccentricity?
circle
The plane is not perpendicular to the axis or parallel to any element and intersects only one nappe.
ellipse
Identify the conic represented by 3x2 - 5y2 - 18x + 20y + 22 = 0.
hyperbola
The plane is parallel to the axis.
hyperbola
Give the standard-form equation of the parabola whose vertex is at the origin and whose focus is (0, 8).
none of the above
Identify the conic represented by 2y2 - x + 8y + 1 = 0.
parabola
The plane is parallel to an element of the surface.
parabola
The plane contains the axis.
two intersecting lines
State the vertex, focus, and directrix of y = -2(x + 1)2 + 3.
vertex: (-1, 3); focus: (-1, 2 7/8); directrix: y = 3 1/8
Write the standard-form equation of the parabola with directrix x = 1 and focus (3, 4).
x = 1/4 (y - 4)2 + 2
Write a standard-form equation of an ellipse with foci (±12, 0) and co-vertices (0, ±5).
x^2/169 + y^2/25 = 1
Which of the following could be the equation of the following graph? Consider the vertex, the y-intercept, and zeros.
y = -(x - 2)2 + 9
Find the standard-form equation of a hyperbola of eccentricity e = 1.25 with center at the origin and vertex (0, 8).
y^2/64 - x^2/36 = 1