Pre-Calculus

• Set of points equidistant from a fixed point (focus) and a fixed line (directrix).

  Parabola
• Length of the latus rectum

  4p
• Equation of the parabola opening upward /downward.

  $(x-h)^2=$$4p(y-k)$
• Equation of the parabola opening to the right.

  $4p(x-h)=$$(y-k)^2$
• Equation of the parabola opening to the left.

  $-4p(x-h)=$$(y-k)^2$
• Set of points whose sum of distances from two fixed points (foci) is a constant.

  Ellipse
• What is the equation of this graph?

  $(x-h)^2/a^2 +$$(y-k)^2/b^2 =$$1$

  
• What is the equation of this graph?

  $(x-h)^2/b^2 +$$(y-k)^2/a^2=$$1$

  
• Set points whose absolute value of difference of distances from two fixed points (foci) is a constant.

  Hyperbola
• What is the equation of this graph?

  $(x-h)^2/a^2 - (y-k)^2/b^2 =$$1$

  
• What is the equation of this graph?

  $(y-k)^2/a^2 - (x-h)^2/b^2 =$$1$