Conics BOB~

The conics section is one of my favorites. There weren't any big surprises and it seemed "short and sweet".

What we learned:

Parabolas

• vertex (h,k), a directrix (straight line, fixed distance from vertex), and focus(fixed distance from vertex)
  
• Standard form VERTICAL:

• Standard form HORIZONTAL:

• When 4p, also known as a, is greater than 1 the parabola is wide.
• When 4p is less than 1 the parabola is skinny.

Circles

• focus= center (h,k)
• Standard form:
• remember, the r is squared.

Ellipses

• center (h,k), Vertices's (endpoints on Major axis), major axis (length of 2a), semi-major axis (length of a, center to one of the vertices's), Minor axis (legnth of 2b), Semi-minor (length b),Foci (c units from center), Focal radi (distance b/w Foci and point on ellipses.
  
• The midpoint of two foci would center of ellipses.
• Standard form HORIZONTAL:
• Standard form VERTICAL:
• a^2 is the bigger number.
  
• c^2 = a^2 - b^2

Hyperbola

• center (h,k), Transverse axis (the distance b/w the vertices's, which are also the vertex. Is the difference of foci to pt, foci2 to pt. length of 2a), semi-transverse axis ( a),conjugate axis (length of 2b), Sem-iconjigate (b), Foci (c units from center), asymptotes.
  
• Standard form HORIZONTAL:
• Standard form VERTICAL:
• c^2 = a^2 + b^2
• When given slope of asymptotes, you can figure out the value of b or a. b/a = rise over run.

When changing equation from general to standard, you'd need to complete the square.

study hard guys!