Page 65 - Standard Handbook Of Petroleum & Natural Gas Engineering

54 Mathematics

Origin at vertex
y2 = 4px
Equation of the directrix
x=h-p
Length of latus rectum
LL' = 4p
Polar equation (focus as origin)
r = p/(1 - cos 0)
Equation of the tangent to y2 = 2 px at (xI,yI)
y,y = P(X + XI)
Equations of an Ellipse of Eccentricity e (Figure 1-41)

(x - h)' (y - k)?
0- +-=1
a2 b2
Coordinates of center C(h,k), of vertices V(h + a,k) and V'(h - a,k), and of
foci F(h + ae,k) and F'(h - ae,k)
Center at origin
x2/a2 + y2/b2 = 1
Equation of the directrices
x = h f a/e
Equation of the eccentricity

Length of the latus rectum
LL' = 2b2/a
Parametric form, replacing x and y by
x = a cos u and y = b sin u
Y

Figure 1-41. Ellipse of eccentricity e.