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MSTE > Analytic Geometry > Flashcards

Analytic Geometry Flashcards

1
Q

The angle that the line makes with the X axis is the angle of inclination of the line, which is equal to the __________.

A

Tangent of the slope (tan theta = slope)

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2
Q

What is translated axis?

A

origin is relocated

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3
Q

How to get the point with respect to the translated axis?

A

(x-xt, y-yt)

note: and origin point sa translated axis ang i minus

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4
Q

Defined by two perpendicular axis

A

cartesian plane

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5
Q

Who invented the cartesian plane

A

Rene Descartes

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6
Q

Distance between two points formula

A

d= sqrt [(x1-x2)^2 + (y1-y2)^2]

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7
Q

Division of Line Segment

A

R= AP/Ab

R= (x-x1)/(x2-x1)
or
R= (y-y1)/(y2-y1)

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8
Q

Midpoint

A

Average of the x and y coordinates

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9
Q

Centroid of a triang;e

A

Average of the coordinates of the vertices

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10
Q

Area of Polygon (coordinate method)

A

A=1/2 (summation of xy)

Mode 32
x y
x1 y2-y3
x2 y3-y1
x3 y1-y2
(Present = Future - Past)

AC > apps > S-Sum

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11
Q

Equation of Lines General Form

A

Ax+By+C=0

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12
Q

Equation of Lines Standard Form

A

Ax+By=C

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13
Q

Slope Intercept Form

A

y= mx+b

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14
Q

Point Slope Form

A

m = (y-y1)/(x-x1)

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15
Q

Two point of form

A

(y2-y1)/(x2-x1) = (y-y1)/(x-x1)

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16
Q

Intercept Form

A

x/a +y/b = 1

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17
Q

Parallel Slope Line Equation

A

m1=m2

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18
Q

Perpendicular Slope Line Equation

A

m2= -1/m1

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19
Q

Angle between 2 lines

A

tan theta = (m2-m1) / 1+m1m2

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20
Q

Distance betweern a point and a line

A

d= abs [Ax+By+C / sqrt (A^2+B^2)]

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21
Q

Distance between 2 lines

A

d= abs [C1-C2 / sqrt (A^2+B^2)]

note: A and B of two lines should have the same coefficient

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22
Q

a set of all points whose location satisfies or is determined by one or more specific conditions

A

Locus of Points

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23
Q

Determining Conic Section: Circle

A

A=C same sign

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24
Q

Determining Conic Section: Ellipse

A

A is not equal to C but has same sign

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25
Q

Determing conic section: parabola

A

Only one (x or y) is squared

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26
Q

Determing conic section: Hyperbola

A

A and C not same sign

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27
Q

Circle General Fomula

A

x^2+y^2+dx+ey+f=0

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28
Q

Circle standard formula

A

(x-h)^2 + (y-k)^2 = r^2

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29
Q

Locus of point equidistant from a fixed point call focus and a fixed line call directrix

A

parabola

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30
Q

How to determine which axis is parabola parallel to

A

the term with 4a in standard from or whichever among x and y is not squared

31
Q

if 4a > 0, parabolaā€¦

A

opens upward or to the right

32
Q

if 4a < 0, parabolaā€¦

A

opens downward or to the left

33
Q

Parabola eccentricity

A

always equal to 1

34
Q

Parabola distance: vertex to focus

A

a

35
Q

Parabola distance: vertex to directrix

A

a

36
Q

Parabola distance: focus to vertex

A

a

37
Q

Parabola distance: Latus rectum

A

4a

38
Q

What is axis of symmetry?

A

line that passes through vertex and focus

39
Q

Parabola standard formula

A

4a(y-k)=(x-h)^2
or
4a(x-h)=(y-k)^2

40
Q

Parabola General Formula

A

Ax^2 + dx + ey + f = 0
or
Cy^2 + dx + ey + f = 0

41
Q

Ellipse general formula

A

Ax^2 + Cy^2 + dx + ey + f =0
(same sign but not same value)

42
Q

Ellipse standard formula

A

(x-h)^2/a^2 + (y-k)^2/b^2 =1

notes
a is always greater than b. kung asa si a. didto ang major axis (orientation of ellipse)

43
Q

Ellipse property:

A

a^2 = b^2 + c^2

44
Q

Eccentricity

A

e = c/a
or
e = a-c / d-a

45
Q

Ellipse distance: center to directix

A

d
d= a/e

46
Q

Ellipse distance: center to focus

A

c

47
Q

Ellipse distance: center to vertex

A

a

48
Q

Ellipse distance: center to covertex

A

b

49
Q

Ellipse distance: major axis

A

2a

50
Q

Ellipse distance: minor axis

A

2b

51
Q

Eccentricity eā€™

A

eā€™= c/b

52
Q

Ellipse distance: Latus Rectum

A

LR= 2b^2/ a

53
Q

Ellipse distance: Flatness

A

f= a-b / a

54
Q

Hyperbola general form

A

Ax^2 + Cy^2 + dx + ey + f =0
(different sign and value)

55
Q

Hyperbola standard form

A

(x-h)^2/a^2 - (y-k)^2/b^2 =1

note: a is always located a the positive term and a dictates where the hyperbola is parallel with

56
Q

Hyperbola property

A

c^2 = a^2 + b^2

57
Q

eccentricity of hyperbola

A

e= c/a
e > 1.0

58
Q

Transverse Axis parallel to x-axis: Asymptote eqn

A

y-k = +/- b/a (x-h)

59
Q

Transverse Axis parallel to y-axis: Asymptote eqn

A

y-k = +/- a/b (x-h)

60
Q

What axis is this parabola parallel with: (x-h)^2/a^2 - (y-k)^2/b^2 =1

A

x-axis

61
Q

What axis is this hyperbola parallel with: (y-k)^2/a^2 - (x-h)^2/b^2 =1

A

y-axis

62
Q

What is transverse axis?

A

the longer axis of the ellipse

63
Q

What is conjugate axis?

A

the shorter axis of the ellipse

64
Q

Polar Coordinates r^2 equation

A

r^2 = x^2 + y^2

65
Q

Polar Coordinates: x =

A

r cos theta

66
Q

Polar Coordinates: y =

A

r sin theta

67
Q

Polar Coordinates: theta is equal to

A

arctan (y/x)

68
Q

Polar Coordinates: Caltech rec to pol

A

Shift +

69
Q

Polar Coordinates: Caltech pol to rec

A

Shift -

70
Q

Polar Coordinates: Caltech getting distance

A

mode 2 (complex)

|x2-x1, < theta 2 - theta 1 |

71
Q

It is a pattern of point that describes its relation to distance of a point (x,y) from one fixed entity to that of another entity.

A

Locus

72
Q

What is the slope of the horizontal line

A

0

73
Q

Another term for slope

A

Inclination

MSTE (7 decks)

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