Stephanie's Reflection

CIRCLES
The equation of a circle in standard form is (x-h)^2-(y-h)^2=r^2 with the center being (h,k) and r being the radius.
Finding the intersection of a line and a circle:
1) solve linear equation for y
2) substitute in circle equation
3) solve for x
4) plug x in to get y value
(if x happens to be imaginary, there is no point of intersection)

EG:
(x-4)^2+(y+2)^2=16
center:(4,-2) radius:4

x^2+y^2+12y+16x-5=0
x^2+16x+64+y^2+12y+36=5+64+36(x+8)^2+(y+6)^2=105
center:(-8,-6) radius:square root of 105

ELLIPSES
1) (x-h)^2/(length of x/2)^2 + (y-k)^2/(length of y/2)^2 =1
2)center is (h,k)
3) major axis has larger denominator
4) vertex is on major axis
5) focus is smaller denom squared = larger denom squared - focus squared
focus is on major axis
Graphing:
1) find center
2) major axis = plus or minus the square root of the bigger denom
3) vertex
4) other intercepts
5) focus
6) length of major axis = 2 square root of
7) length of minor axis = 2 square root of
8) graph

EG:
x^2/4+y^2/1=1
1) (0,0)
2) x
3) +/-2 (2,0) (-2,0)
4) +/-1 (0,1) (0,-1)
5) 1=4-c^2 c=+/-square root of 3 (sr3,0) (-sr3,0)
6) 2 square root of 4 = 4
7) 2 square root of 1
8) graph

HYPERBOLAS
1) (x+h)^2/(length/2)^2 - (y-k)^2/(length/2)^2 =1
OR
-(x-h)^2/(length/2)^2 + (y-k)^2/(length/2)^2 =1
2) center (h,k)
3) major axis is non-negative
4) vertex is the square root of non-negative denom
5) asymptotes y=+/-(square root of y)/(square root of x)x
6) focus^2 = x denom + y denom
focus^2 = vertex^2 + other denom

to sketch:
1) shape
2) center
3) major
4) minor
5) other intercept - none for hyperbolas
6) focus
7) asymptotes y=+/-square root of y/square root of x
8) vertex
9) sketch
A) draw a box using the vertex and +/-sr of other denom
B) draw diagonal through box corners
C) sketch a parabola on each vertex
D) label focus and asymptotes

EG:
x/36-y/9=1
2) (0,0)
3) x
4) y
5) none
6) c^2=36+9 c^2=45 c=sr45 (sr45,0) (-sr45,0)
7) y=+/-square root of 5/square root of 6
8) +/-sr36 = +/-6 (6,0) (-6,0)
9) sketch

Yes, I get that if I don't understand something to look in my notes but I wasn't there to hear the explanation of circles so my notes don't really help me. I'd really appreciate it if someone would explain.