Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 10

Distance $d$ between Two Points $\map {P_1} {x_1, y_1}$ and $\map {P_2} {x_2, y_2}$

 * $10.1$: Distance Formula

Slope $m$ of Line Joining Two Points $\map {P_1} {x_1, y_1}$ and $\map {P_2} {x_2, y_2}$

 * $10.2$: Slope of Straight Line joining Points in Cartesian Plane

Equation of Line Joining Two Points $\map {P_1} {x_1, y_1}$ and $\map {P_2} {x_2, y_2}$

 * $10.3$: Two-Point Form
 * $10.4$: Slope-Intercept Form

Equation of Line in terms of $x$ Intercept $a \ne 0$ and $y$ Intercept $b \ne 0$

 * $10.5$: Two-Intercept Form

Normal Form for Equation of Line

 * $10.6$: Normal Form

General Equation of Line

 * $10.7$: General Equation

Distance from Point $\tuple {x_1, y_1}$ to Line $A x + B y + C = 0$

 * $10.8$: Perpendicular Distance from Straight Line in Plane to Point

Angle $\psi$ between Two Lines having Slopes $m_1$ and $m_2$

 * $10.9$: Angle between Straight Lines in Plane
 * Parallel Straight Lines have Same Slope
 * Product of Slopes of Perpendicular Lines is $-1$

Area of Triangle with Vertices at $\tuple {x_1, y_1}$, $\tuple {x_2, y_2}$, $\tuple {x_3, y_3}$

 * $10.10$: Area of Triangle in Determinant Form

Transformation of Coordinates involving Pure Translation

 * $10.11$: Translation of Cartesian Coordinates

Transformation of Coordinates involving Pure Rotation

 * $10.12$: Rotation of Cartesian Coordinates

Transformation of Coordinates involving Translation and Rotation

 * $10.13$: Translation and Rotation of Cartesian Coordinates

Polar Coordinates $\tuple {r, \theta}$

 * $10.14$: Conversion between Cartesian and Polar Coordinates in Plane

Equation of Circle of Radius $R$, Center are $\tuple {x_0, y_0}$

 * $10.15$: Equation of Circle in Cartesian Plane

Equation of Circle of Radius $R$ Passing through Origin

 * $10.16$: Equation of Circle in Cartesian Plane passing through Origin

Conics [Ellipse, Parabola or Hyperbola]

 * Definition:Conic Section: Focus-Directrix Property
 * Definition:Conic Section: Intersection with Cone


 * $10.17$: Polar Equation of Conic with Focus at Origin


 * Eccentricity of Conic Section determines Type