ANALYTIC GEOMETRY
RECTANGULAR COORDINATES
DISTANCE
- The distance d between two points, P 1 (x 1 , y 1 ) and P 2 (x 2 , y 2 ), is given by
EQUATIONS OF THE STRAIGHT LINE
- POINT-SLOPE FORM. Through P 1 (x 1 , y 1 ) and with slope m:
y − y 1 = m(x − x 1 ).- SLOPE-INTERCEPT FORM. With slope m and y-intercept b:
y = mx + b. - TWO-POINT FORM. Through P 1 (x 1 , y 1 ) and P 2 (x 2 , y 2 ):
- 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 the y-
intercept, the x-intercept,
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
- 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).