Page 66 - Standard Handbook Of Petroleum & Natural Gas Engineering

Analytic Geometry 55

Polar equation (focus as origin)
r = p/(l - e cos e)
Equation of the tangent at (xI,yI)
b2xlx + a2y,y = a2b2

Equations of a Hyperbola (Figure 1-42)

(x-h)'
0 ---=I (Y-k)'
a2 b2
Coordinates of the center C(h,k), of vertices V(h + a,k) and V'(h - a,k),
and of the foci F(h + ae,k) and F'(h - ae,k)
Center at origin
x2/a2 - y2/b2 = 1
Equation of the directrices
x = h * a/e
Equation of the asymptotes
y - k = k b/a (x - k)
Equation of the eccentricity
da2 + b2 ,
e=
a
Length of the latus rectum
LL' = 2b2/a
Parametric form, replacing x and y
x = a cosh u and y = b sinh u
Polar equation (focus as origin)
r = p/(1 - e cos e)

Y

Figure 1-42. Equation of a hyperbola.