The Ungerecht Family Tree

vertex of a parabola: for y = ax^2 + bx + c, then x = -b/2a

standard form of a parabola:

(x-h)² = 4p(y-k)  => if p>0, opens up, p<0 opens down
(y-k)² = 4p(x-h)  => if p>0, opens to right, p<0 opens to left  
where point (h,k) is the vertex, and 
 p = minimum distance between parabola and vertex (is on axis of symmetry,
     which is perpendicular to the directrix)
this can be rewritten as:
  y = (1/4p)(x-h)² + k for an up/down parabola
  x = (1/4p)(y-k)² + h for a left/right parabola
LR (latus rectum line) is line parallel to directrix going thru focus (if you know focus, 
easy to find LR points and vertex, then draw the function). Length of LR is |4p|

Standard form of a circle:

(x-h)² + (y-k)² = r²
where point (h,k) is the center, and r is radius
This can be expanded to x² + y² + Dx + Ey + F = 0  (aka the General form)
Can go from general form to standard form by completing the square

Ellipse - sum of distance from two foci is a constant

points on the ellipse follow the formula:
  (x-h)²/a² + (y-k)²/b² = 1
and
   c² = a² - b²
center C = (h,k)
a = distance from C to long end of ellipse (along major axis)
b = distance from C to close end of ellipse (along minor axis)
c = distance from center to a focus
(x,y) = a point on the ellipse

Hyperbola - difference of distance from two foci is a constant

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