Equation of a circle In an x−y coordinate system, the circle with center (a,b) and radius r is the set of all points (x,y) such that: \( (x-a)^2 + (y-b)^2 =r^2 \) Circle centered at the origin: \( x^2 + y^2 = r^2 \) Parametric equations \( \begin{aligned} x &= a + r\,\cos t \\ y&= b + […]

## MathJax Quick Start Tutorial

About MathJax MathJax is a cross-browser JavaScript library that displays mathematical equations in web browsers, using MathML, LaTeX and ASCIIMathML markup. MathJax is released as open-source software under the Apache license. MathJax downloads with web page content, scans the page content for equation markup, and typesets the math. Thus, MathJax requires no installation of software […]

## Triangles in Two Dimensions

Area of the triangle The area of the triangle formed by the three lines: \( \begin{aligned} A_1x + B_1y + C_1 &= 0 \\ A_2x + B_2y + C_2 &= 0 \\ A_3x + B_3y + C_3 &= 0 \end{aligned} \) is given by \( A = \frac{\begin{vmatrix} A_1 & B_1 & C_1 \\ A_2 […]

## Common Derivatives Formulas

Basic Properties of Derivatives \( \left(c \cdot f(x)\right)’ = c \cdot f'(x) \) \( \left(f \pm g \right)’ = f’ \pm g’ \) Product rule \( (f \cdot g)’ = f’ \cdot g + f \cdot g’ \) Quotient rule \( \left( \frac{f}{g} \right)’ = \frac{ f’\cdot g – f \cdot g’ }{g^2} \) Chain rule \( \left( f […]

## Lines in Two Dimensions

Line forms Slope y-intercept form: \( y = mx+b \) Two point form: \( y – y_1 =\frac{y_2-y_1}{x_2 – x_1} (x – x_1) \) Point slope form: \( y – y_1 = m(x – x_1) \) Intercept form: \( \frac{x}{a} + \frac{y}{b} = 1~,~(a,b \ne 0) \) Normal form: \( x\cdot \cos\Theta + y\cdot \sin\Theta = p \) Parametric form: […]