1. The Circle x2+y2+2gx+2fy+c = 0 (x-a)2 + (y-b)2 = r2 x2 + y2 = r2
Graph Sketching
b2 - 4ac < 0
2 pts of intersection
Move the circle from the origin a units to the right
b units upwards
Used for intersection problems between circles and lines
Factorisation
b2 - 4ac < 0
No intersection
x2+y2+2gx+2fy+c = 0
Centre
(a,b)
Centre
(-g,-f)
b2 - 4ac = 0
1 pt of intersection
TANGENT to circle
The
Circle
(x-a)2 + (y-b)2 = r2
Straight line
Theory
Pythagoras Theorem rotated through 360o
x2 + y2 = r2
Perpendicular
Equation
m1xm2 = -1
Two circles touch externally if the distance
C1C2=(r1 + r2)
Distance Formula
Two circles touch internally if the distance
C1C2=(r1 - r2)
Centre
(0,0)