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

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## Murray R. Spiegel:

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

Published $\text {1968}$

## $10 \quad$ Formulas from Plane Analytic Geometry

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

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

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

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

### Normal Form for Equation of Line

### General Equation of Line

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

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

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

### Transformation of Coordinates involving Pure Translation

### Transformation of Coordinates involving Pure Rotation

### Transformation of Coordinates involving Translation and Rotation

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

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

### Equation of Circle of Radius $R$ Passing through Origin

### Conics [Ellipse, Parabola or Hyperbola]

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

### 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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