a brief summary of coordinate geometry, parabolae, etc

see also:

• a brief summary of mathematical principles and tools
• History of Mathematics
• mensuration - how to measure area, volume, etc of various shapes
• Algebra
• Calculus
• Circular functions

• equation y = mx + c;
• gradient between two points (x₁,y₁) and (x₂,y₂) is m = (y₂ - y₁) / (x₂ - x₁) 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;

• 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'));

• equation: f(x) = ax² + 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 = b² - 4ac;
• to solve quadratic functions where D is negative, requires use of complex numbers to give “imaginary” solutions

• (x-h)² + (y-k)² = r², where r = radius, (h,k) centre;

• general equation: x² / a² + y² / b² = 1,
• foci: (+/-ae,0), DD': x = +/-a/e, 0<e<1,
• b² = a²(1-e²);

• general equation: x² / a² - y² / b² = 1,
• foci: (+/-ae,0), DD': x = +/-a/e, e>1,
• b² = a²(e²-1);

• general equation: y² = 4ax,
• foci: (a,0) DD': x = -a, e=1,