Analytical Geometry

Question 1

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

Answer 1

Question 2

Distance between two points

Answer 2

Question 3

Midpoint of two points

Answer 3

Question 4

Distance between a point and a line

Answer 4

Question 5

Distance between two parallel lines

Answer 5

Question 6

Slope of a line

Answer 6

Question 7

Relationship between the slope of two parallel lines

Answer 7

Question 8

Relationship between the slope of two perpendicular lines

Answer 8

Question 9

Angle of inclination of a line

Answer 9

Question 10

Angle between two lines
For acute:
For Obtuse:

Answer 10

Question 11

Area of a triangle given 3 points (Calculator Method)

Answer 11

Question 12

Centroid given 3 points

Answer 12

Question 13

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

Answer 13

Circle

Question 14

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

Answer 14

Question 15

Circle
Eccentricity:
Area:
Circumference:

Answer 15

Question 16

Answer 16

Parabola

Question 17

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

Answer 17

Question 18

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

Answer 18

Question 19

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

Answer 19

Question 20

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

Answer 20

Question 21

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

Answer 21

Question 22

Answer 22

Ellipse

Question 23

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

Answer 23

Question 24

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

Answer 24

Question 25

Ellipse Relationship between a, b, and c

Answer 25

Question 26

Ellipse Eccentricity: Length of Latus Rectum:

Answer 26

Question 27

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

Answer 27

Question 28

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

Answer 28

Question 29

Ellipse Area: Perimeter:

Answer 29

Question 30

Answer 30

Hyperbola

Question 31

Hyperbola General Equation

Answer 31

Question 32

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

Answer 32

Question 33

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

Answer 33

Question 34

Relationship between a, b, and c of hyperbola

Answer 34

Question 35

Hyperbola Eccentricity: Length of Latus Rectum:

Answer 35

Question 36

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

Answer 36

Question 37

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

Answer 37

Question 38

Hyperbola Equations of Asymptote:

Answer 38

Question 39

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

Answer 39

Question 40

Polar to Cartesian Conversions:

Answer 40

Question 41

Distance between two points in polar coordinate system

Answer 41

Question 42

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

Answer 42

Question 43

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

Answer 43

Question 44

Polar Equation of a line

Answer 44

Question 45

Polar Equation of a Circle

Answer 45

Question 46

Polar Equation of Conics (Parabola, Ellipse, Hyperbola)

Answer 46

Question 47

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

Answer 47

Question 48

General Equation of Plane

Answer 48

Question 49

Intercept form of a plane

Answer 49

Question 50

Area of the first octant part of the plane

Answer 50

Question 51

Volume of solids bounded with the the coordinate planes

Answer 51

Question 52

Equation of a plane passing through 3 points

Answer 52

Question 53

Distance between two points of a plane

Answer 53

Question 54

Midpoint between two points of a plane

Answer 54

Question 55

Distance from a point to a plane

Answer 55

Question 56

Distance between parallel planes

Answer 56

Question 57

Angle between two planes

Answer 57

Question 58

Equation of a sphere

Answer 58

Question 59

General form of vector

Answer 59

Vector = Ai + Bj + Ck

Question 60

Absolute Value of Vector

Answer 60

Question 61

Dot (scalar) product of vectors (2 equations)

Answer 61

Question 62

Cross (Vector) Product

Answer 62

Question 63

Unit Vector formula

Answer 63

Question 64

Angle between two vectors

Answer 64

Question 65

Area of triangle given vector

Answer 65