INTERCEPT FORM. With x- and y-intercepts of a and b, respectively:
GENERAL FORM. Ax + By + C = 0, where A and B are not both zero. If B ≠
0, the slope is
DISTANCE FROM POINT TO LINE
Distance d between a point P (x 1 , y 1 ) and the line Ax + By + C = 0 is
EQUATIONS OF THE CONICS
CIRCLE
With center at (0, 0) and radius r: x 2 + y^2 = r 2.
With center at (h, k) and radius r: (x − h)^2 + (y − k)^2 = r^2.
PARABOLA
With vertex at (0, 0) and focus at (p, 0): y^2 = 4px.
With vertex at (0, 0) and focus at (0, p): x^2 = 4py.
With vertex at (h, k) and axis
parallel to x-axis, focus at (h + p, k): (y − k)^2 = 4p(x − h).
parallel to y-axis, focus at (h, k + p): (x − h)^2 = 4p(y − k).
ELLIPSE
With major axis of length 2a, minor axis of length 2b, and distance
between foci of 2c:
Center at (0, 0), foci at (±c, 0), and vertices at (±a, 0):
Center at (0, 0), foci at (0, ±c), and vertices at (0, ±a):
