PC Conics

Circle function fomrula

• Distance formula

• Midpoint formula

x²+y²=r²

m = (x1 + x2)/2 , (y1+y2)/2

Ellipses

• major axis =

• major axis along x-axis formula

• major axis y-axis formula

• center

• foci formula

Ex.)

• major axis = biggest axis

• X axis, Y Axis

  

• center: c² = a² - b²

• foci: (h, k±c) or (h±c, k)

Ex.)

Parabolas

• opens up/down and opens right/left formulas

• directrix =

• latus rectum =

Ex.)

• formulas

  • up/down: (x-h)² = ±4p(y-k)

  • right/left: (y-k)² = ±4p(x-h)

• line that is p distance away from vertex

• line going through foci and has endpoints on the curve, 4p total

Ex.)

Hyperbola

• transverse axis =

• foci =

• formula for transverse axis parallel to the x axis

• fomula for transverse axis parallel to the y axis

• asymptotes for horizontal:

• asymptotes for vertical:

Ex.)

the box one

• connects the two vertices (NOT ALWAYS THE BIGGEST)

• inside the the curve, c distance away from the center

• look at pic

• look at pic

• asymptotes for horizontal: (y-k) = ± b/a (x-h)

• asymptotes for vertical: (y-k) = ± a/b (x-h

Ex.)

Inequalities

• How do you know how to shade an inequality?

ex.) x²+y²>9 and x+y <3

ex.) write a system of inequalities for the pic

TEST A POINT ABOVE OR BELOW THE LINE!!!!

ex.) should be UNDER the line and to the left