Analytic Geometry

Question 1

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

Answer 1

Tangent of the slope (tan theta = slope)

Question 2

What is translated axis?

Answer 2

origin is relocated

Question 3

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

Answer 3

(x-xt, y-yt)

note: and origin point sa translated axis ang i minus

Question 4

Defined by two perpendicular axis

Answer 4

cartesian plane

Question 5

Who invented the cartesian plane

Answer 5

Rene Descartes

Question 6

Distance between two points formula

Answer 6

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

Question 7

Division of Line Segment

Answer 7

R= AP/Ab

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

Question 8

Midpoint

Answer 8

Average of the x and y coordinates

Question 9

Centroid of a triang;e

Answer 9

Average of the coordinates of the vertices

Question 10

Area of Polygon (coordinate method)

Answer 10

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

Question 11

Equation of Lines General Form

Answer 11

Ax+By+C=0

Question 12

Equation of Lines Standard Form

Answer 12

Ax+By=C

Question 13

Slope Intercept Form

Answer 13

y= mx+b

Question 14

Point Slope Form

Answer 14

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

Question 15

Two point of form

Answer 15

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

Question 16

Intercept Form

Answer 16

x/a +y/b = 1

Question 17

Parallel Slope Line Equation

Answer 17

m1=m2

Question 18

Perpendicular Slope Line Equation

Answer 18

m2= -1/m1

Question 19

Angle between 2 lines

Answer 19

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

Question 20

Distance betweern a point and a line

Answer 20

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

Question 21

Distance between 2 lines

Answer 21

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

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

Question 22

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

Answer 22

Locus of Points

Question 23

Determining Conic Section: Circle

Answer 23

A=C same sign

Question 24

Determining Conic Section: Ellipse

Answer 24

A is not equal to C but has same sign

Question 25

Determing conic section: parabola

Answer 25

Only one (x or y) is squared

Question 26

Determing conic section: Hyperbola

Answer 26

A and C not same sign

Question 27

Circle General Fomula

Answer 27

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

Question 28

Circle standard formula

Answer 28

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

Question 29

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

Answer 29

parabola

Question 30

How to determine which axis is parabola parallel to

Answer 30

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

Question 31

if 4a > 0, parabola...

Answer 31

opens upward or to the right

Question 32

if 4a < 0, parabola...

Answer 32

opens downward or to the left

Question 33

Parabola eccentricity

Answer 33

always equal to 1

Question 34

Parabola distance: vertex to focus

Answer 34

a

Question 35

Parabola distance: vertex to directrix

Answer 35

a

Question 36

Parabola distance: focus to vertex

Answer 36

a

Question 37

Parabola distance: Latus rectum

Answer 37

4a

Question 38

What is axis of symmetry?

Answer 38

line that passes through vertex and focus

Question 39

Parabola standard formula

Answer 39

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

Question 40

Parabola General Formula

Answer 40

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

Question 41

Ellipse general formula

Answer 41

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

Question 42

Ellipse standard formula

Answer 42

(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)

Question 43

Ellipse property:

Answer 43

a^2 = b^2 + c^2

Question 44

Eccentricity

Answer 44

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

Question 45

Ellipse distance: center to directix

Answer 45

d d= a/e

Question 46

Ellipse distance: center to focus

Answer 46

c

Question 47

Ellipse distance: center to vertex

Answer 47

a

Question 48

Ellipse distance: center to covertex

Answer 48

b

Question 49

Ellipse distance: major axis

Answer 49

2a

Question 50

Ellipse distance: minor axis

Answer 50

2b

Question 51

Eccentricity e'

Answer 51

e'= c/b

Question 52

Ellipse distance: Latus Rectum

Answer 52

LR= 2b^2/ a

Question 53

Ellipse distance: Flatness

Answer 53

f= a-b / a

Question 54

Hyperbola general form

Answer 54

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

Question 55

Hyperbola standard form

Answer 55

(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

Question 56

Hyperbola property

Answer 56

c^2 = a^2 + b^2

Question 57

eccentricity of hyperbola

Answer 57

e= c/a e > 1.0

Question 58

Transverse Axis parallel to x-axis: Asymptote eqn

Answer 58

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

Question 59

Transverse Axis parallel to y-axis: Asymptote eqn

Answer 59

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

Question 60

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

Answer 60

x-axis

Question 61

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

Answer 61

y-axis

Question 62

What is transverse axis?

Answer 62

the longer axis of the ellipse

Question 63

What is conjugate axis?

Answer 63

the shorter axis of the ellipse

Question 64

Polar Coordinates r^2 equation

Answer 64

r^2 = x^2 + y^2

Question 65

Polar Coordinates: x =

Answer 65

r cos theta

Question 66

Polar Coordinates: y =

Answer 66

r sin theta

Question 67

Polar Coordinates: theta is equal to

Answer 67

arctan (y/x)

Question 68

Polar Coordinates: Caltech rec to pol

Answer 68

Shift +

Question 69

Polar Coordinates: Caltech pol to rec

Answer 69

Shift -

Question 70

Polar Coordinates: Caltech getting distance

Answer 70

mode 2 (complex) |x2-x1, < theta 2 - theta 1 |

Question 71

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.

Answer 71

Locus

Question 72

What is the slope of the horizontal line

Answer 72

0

Question 73

Another term for slope

Answer 73

Inclination