maths:coordinate

### Table of Contents

# a brief summary of coordinate geometry, parabolae, etc

see also:

## Introduction

## Straight Line:

- equation y = mx + c;
- gradient between two points (x
_{1},y_{1}) and (x_{2},y_{2}) is m = (y_{2}- y_{1}) / (x_{2}- x_{1}) ie. “rise over run” - Y-intercept = c;
- equation of perpendicular line intersecting at (a,b):
- gradient m' = 1/m;
- ⇒ y' = x'/m + (b - a/m);

- intersection of 2 lines:
- Solve with simultaneous equations;

#### Division of a Line Segment in a given ratio:

- if A,B are 2 points on a line whose coords are (x,y) & (x',y') respectively, then the coords. of the point which divides AB internally in the ration m:m' are:
- ((mx'+m'x)/(m+m'), (my'+m'y)/(m+m'));

## Quadratic Functions:

- equation: f(x) = ax
^{2}+ bx + c, a <> 0; - has a minimum value if a>0, a maximum value if a<0;
- when f(x)=0, x = (-b + SQR(D))/2a, and, x = (-b - SQR(D))/2a, where D = b
^{2}- 4ac; - to solve quadratic functions where D is negative, requires use of complex numbers to give “imaginary” solutions

## Circle:

- (x-h)
^{2}+ (y-k)^{2}= r^{2}, where r = radius, (h,k) centre;

## Ellipse:

- general equation: x
^{2}/ a^{2}+ y^{2}/ b^{2}= 1, - foci: (+/-ae,0), DD': x = +/-a/e, 0<e<1,
- b
^{2}= a^{2}(1-e^{2});

## Hyperbola:

- general equation: x
^{2}/ a^{2}- y^{2}/ b^{2}= 1, - foci: (+/-ae,0), DD': x = +/-a/e, e>1,
- b
^{2}= a^{2}(e^{2}-1);

## Parabola:

- general equation: y
^{2}= 4ax, - foci: (a,0) DD': x = -a, e=1,

maths/coordinate.txt · Last modified: 2021/07/24 11:39 by gary1