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

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

Published $\text {1968}$.


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$10 \quad$ Formulas from Plane Analytic Geometry

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


Ellipse with Center $\map C {x_0, y_0}$ and Major Axis Parallel to $x$ Axis

Parabola with Axis Parallel to $x$ Axis

Hyperbola with Center $\map C {x_0, y_0}$ and Major Axis Parallel to $x$ Axis

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