Math: Chapter 9 Review

midpoint formula

M(x,y) = ((x1+x2)/2 , (y1+y2)/2)

distance formula

square root sign w/ (x1-x2)+2 + (y1-y2)+2 underneath

parabola equations

1 sq term opens vertically: y-k = (x-h)+2 if a>0 up, if a<0 down a=1/4c vertex: (h,k) fp: (h, k+c) dir: y=k-c axis: x=h c=v-->fp opens horizontally: x-h = (y-k)+2 if a>0 right, a<0 left a=1/4c vertex: (h,k) fp: (h+c,k) dir: x=h-c axis: y=k c=v-->fp

perpendicular bisector

first point w/ distance formula equals the second point w/ distance formula

equation systems

solutions - points of intersection

circle equation

sq term coefficients are identical (x-h)+2 + (y-k)+2 = r+2 center: (h,k) radius = r

ellipse equations

sq term coefficients are same sign, but different values (x-h)+2/a+2 + (y-k)+2/b+2 = 1 (a>b & c goes w/ a) (x-h)+2/b+2 + (y-k)+2/a+2 = 1 (a>b & c goes w/ a) center: (h,k) c+2 = a+2 - b+2 sum of focal radii = 2a

hyperbola equations

sq term coefficients have 1+ and 1- (x-h)+2 - (y-k)+2 = 1 (y-k)+2 - (x-h)+2 = 1 x+2 - y+2 = 1 --> y = +- (b/a)x y+2 - x+2 = 1 --> y = +- (a/b)x a = positive b = negative c+2 = a+2 = b+2 difference of focal radii = 2a

line equation

y = mx + b