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M > Analytical Geometry > Flashcards

Analytical Geometry Flashcards

1
Q

Line
General Equation:
Two-point form:
Point-slope form:
slope-intercept form:
Intercept form:

A
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2
Q

Distance between two points

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3
Q

Midpoint of two points

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4
Q

Distance between a point and a line

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5
Q

Distance between two parallel lines

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6
Q

Slope of a line

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7
Q

Relationship between the slope of two parallel lines

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8
Q

Relationship between the slope of two perpendicular lines

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9
Q

Angle of inclination of a line

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10
Q

Angle between two lines
For acute:
For Obtuse:

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11
Q

Area of a triangle given 3 points (Calculator Method)

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12
Q

Centroid given 3 points

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13
Q

locus of point that which moves so that it is equidistant from a fixes point called center

A

Circle

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14
Q

Circle
General Equation:
Standard Equation, center at (0,0)
Standard Equation, center at (h,k)

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15
Q

Circle
Eccentricity:
Area:
Circumference:

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16
Q
A

Parabola

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17
Q

Parabola General Equation
Axis Parallel to the y-axis:
Axis Parallel to the x-axis:

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18
Q

Parabola
Standard Equation, vertex at (0,0)
a. Axis along the y-axis
b. A is along the x-axis

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19
Q

Parabola
Standard Equation, vertex at (h,k)
a. Axis Parallel to the y-axis
b. Axis Parallel to the x-axis

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20
Q

Parabola
Eccentricity:
Length of Latus Rectum:
Distance from vertex to directrix:
Distance from vertex to focus:

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21
Q

Parabola
Distance from focus to directrix:
Area of Parabolic segment:

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22
Q
A

Ellipse

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23
Q

Ellipse
1.General Equation:
2. Standard Equation, c(0,0)
a. Major axis along the y-axis:
b. Major Axis along the x-axis:

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24
Q

Ellipse
Standard Equation, c(h,k)
a. Major axis parallel to y-axis
b. Major axis parallel to x-axis

A
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25
Q

Ellipse
Relationship between a, b, and c

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26
Q

Ellipse
Eccentricity:
Length of Latus Rectum:

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27
Q

Ellipse
Length of Major axis:
Length of semi-major axis:
Length of minor axis:
length of semi-minor axis:

A
28
Q

Ellipse
Distance between foci:
distance from center to focus (focal distance):
distance from center to directrix:

A
29
Q

Ellipse
Area:
Perimeter:

A
30
Q
A

Hyperbola

31
Q

Hyperbola General Equation

A
32
Q

Hyperbola Standard Equation C(0,0)
a. Transverse axis along the y-axis
b. transverse axis along the x-axis

A
33
Q

Hyperbola
Standard Equation C(h,k)
a. Transverse axis parallel to y-axis
b. Transverse axis parallel to x-axis

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34
Q

Relationship between a, b, and c of hyperbola

A
35
Q

Hyperbola
Eccentricity:
Length of Latus Rectum:

A
36
Q

Hyperbola
Length of Transverse axis:
Length of semi-transverse axis:
Length of conjugate axis:
Length of semi-conjugate axis:

A
37
Q

Hyperbola
Distance between foci:
distance between center to focus (focal distance):
distance from center to the directrix:

A
38
Q

Hyperbola
Equations of Asymptote:

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39
Q

Polar coordinate system
conversion of cartesian to polar
x =
y =

A
40
Q

Polar to Cartesian Conversions:

A
41
Q

Distance between two points in polar coordinate system

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42
Q

In the General Equation below, it is
Circle:
Ellipse:
Hyperbola:
when

A
43
Q

In the equation below, it is
Parabola if:
Ellipse if:
Hyperbola if:

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44
Q

Polar Equation of a line

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45
Q

Polar Equation of a Circle

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46
Q

Polar Equation of Conics (Parabola, Ellipse, Hyperbola)

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47
Q

In the Equation below, it is
Parabola if:
Ellipse if:
Hyperbola if:

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48
Q

General Equation of Plane

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49
Q

Intercept form of a plane

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50
Q

Area of the first octant part of the plane

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51
Q

Volume of solids bounded with the the coordinate planes

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52
Q

Equation of a plane passing through 3 points

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53
Q

Distance between two points of a plane

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54
Q

Midpoint between two points of a plane

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55
Q

Distance from a point to a plane

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56
Q

Distance between parallel planes

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57
Q

Angle between two planes

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58
Q

Equation of a sphere

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59
Q

General form of vector

A

Vector = Ai + Bj + Ck

60
Q

Absolute Value of Vector

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61
Q

Dot (scalar) product of vectors (2 equations)

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62
Q

Cross (Vector) Product

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63
Q

Unit Vector formula

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64
Q

Angle between two vectors

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65
Q

Area of triangle given vector

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M (12 decks)

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