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問題一覧
1
What is the name for the x-coordinate?
abscissa
2
What is the name for the y-coordinate?
ordinate
3
What is the name of the center of a coordinate system?
origin
4
What is the midpoint formula?
midpoint = ((x1 + x2)/2, (y1 + y2)/2)
5
What is the distance formula?
d = sqrt((x2 - x1)² + (y2 - y1)²)
6
What is the area of a circle?
A = pi × r²
7
What is the formula for finding the slope of a line?
m = (y2 - y1)/(x2 - x1)
8
What is the slope-intercept form?
y = mx + b
9
What is the point-slope form?
y - y1 = m(x - x1)
10
What is the two-point form?
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
11
What is the formula for finding the inclination of a line?
theta = tan‐¹((y2-y1)/(x2-x1))
12
What is the formula for finding the angle between two lines?
theta = tan‐¹((m1 - m2)/(1 + m1m2))
13
What is the equation of the slopes of two parallel lines?
m1 = m2
14
What is the equation of the slopes of two perpendicular lines?
m1 = -1/m2
15
Which of the following is perpedicular to Ax + By + C1 = 0?
Ax - By + C2 = 0
16
Which of the following is parallel to Ax + By + C1 = 0?
Ax + By + C2 = 0
17
What is the formula for the eccentricity of a conic section?
e = f/d
18
What divides the conic section symmetrically?
principal axis
19
What is the line perpendicular to the axis of symmetry and does not pass through the conic section?
directrix
20
What is the eccentricity of a circle?
e = 0
21
What is the eccentricity of an ellipse?
e < 1
22
What is the eccentricity of a parabola?
e = 1
23
What is the eccentricity of a hyperbola?
e > 1
24
What is the fixed point in a conic section?
focus
25
What is the eccentricity of a line?
e = infinite
26
What is the general equation of an inclined conic section?
Ax² + Bxy + Cy² + Dx + Ey + F = 0
27
What is the general equation of both vertical and horizontal conic sections?
Ax² + Cy² + Dx + Ey + F = 0
28
What is the formula for the discriminant of a conic section?
delta = B² - 4AC
29
What is the discriminant of a hyperbola?
delta > 0
30
What is the discriminant of a parabola?
delta = 0
31
What is the discriminant of an ellipse?
delta < 0
32
What is the discriminant of a circle?
delta < 0
33
What is the point of intersection between a parabola and the principal axis?
vertex
34
What commonly denotes the vertex in a parabola?
(h, k)
35
What is the line segment that is parallel to the directrix and passes through the focus with both endpoints on the parabola?
latus rectum
36
What is the length of the latus rectum?
LR = 4a, where a is the distance from the focus to the vertex
37
What is the general equation of parabola with a vertical principal axis?
Ax² + Dx + Ey + F = 0
38
What is the general equation of a parabola with a horizontal principal axis?
Cy² + Dx + Ey + F = 0
39
What is the standard equation of a parabola with a vertical principal axis?
(x - h)² = ±4a(y - k)
40
What is the standard equation of a parabola with a horizontal principal axis?
(y - k)² = ±4a(x - h)
41
From the equation (x - h)² = 4a(y - k), 4a should be ______ for the parabola to open upward.
positive
42
From the equation (y - k)² = ±4a(x - h), 4a should be _____ for the parabola to open to the left.
negative
43
What is the general equation of a circle?
Ax² + Cy² + Dx + Ey + F = 0
44
What is the standard equation of a circle?
(x - h)² + (y - k)² = r²
45
What is the formula for finding the center of a circle?
(h, k) = (-D/2A, -E/2C)
46
What is the formula for finding the radius of the circle?
r = sqrt(h² + k² - (F/A))
47
What is the general equation of an ellipse?
Ax² + Cy² + Dx + Ey + F = 0
48
What is the formula for finding the center of an ellipse?
(h, k) = (-D/2A, -E/2C)
49
What is the standard equation of an ellipse with a horizontal principal axis?
(x - h)²/a² + (y - k)²/b² =1, where a is the semi-major axis (longer line) and b is the semi-minor axis (shorter line).
50
What is the standard equation of an ellipse with a vertical principal axis?
(y - k)²/a² + (x - h)²/b² =1, where a is the semi-major axis (longer line) and b is the semi-minor axis (shorter line).
51
What is the equation for finding the eccentricity of an ellipse?
e = a/d or e = c/a, where a is the semi-major axis (longer line), c is the line from center to the focus and d is the line from center to the directrix.
52
What is the equation for finding the latus rectum of an ellipse?
LR = 2b²/a, where a is the semi-major axis (longer line) and b is the semi-minor axis (shorter line).
53
What is the general equation of a hyperbola?
±Ax² ‐+ Cy² + Dx + Ey + F = 0
54
What is the standard equation of the hyperbola with a vertical principal axis?
(y - k)²/a² - (x - h)²/b² = 1, where the denominator a² is always on the positive term and the denominator b² is always on the negative term.
55
What is the standard equation of the hyperbola with a horizontal principal axis?
(x - h)²/a² - (y - k)²/b² = 1, where the denominator a² is always on the positive term and the denominator b² is always on the negative term.
56
What is the formula for finding the center of a hyperbola?
(h, k) = (-D/2A, -E/2C)
57
What is the equation for finding the eccentricity of a hyperbola?
e = a/d or e = c/a, where a is the line from the center to the vertex, c is the line from center to the focus and d is the line from center to the directrix.
58
What is the equation for finding the latus rectum of a hyperbola?
LR = 2b²/a, where a is the line from the center to the vertex and b is the line from the vertex to the asymptote.
59
What is the equation for finding the asymptotes of a hyperbola with a horizontal principal axis?
y-k = m(x - h) in which m = ±b/a, where a is the line from the center to the vertex and b is the line from the vertex to the asymptote.
60
What is the equation for finding the asymptotes of a hyperbola with a vertical principal axis?
y-k = m(x - h) in which m = ±a/b, where a is the line from the center to the vertex and b is the line from the vertex to the asymptote.