Page 63 - Standard Handbook Of Petroleum & Natural Gas Engineering

52 Mathematics

then the equation of the line tangent to the curve at this point is

and the normal to the curve is the line perpendicular to the tangent with slope
m2 where

m2 = -I/m, = -I/f'(x)
or

Equations of a Straight Line
General equation
ax + by + c - 0
9 Intercept equation
x/a + y/b = 1
Normal form (Figure 1-39)
x cos 8 + y sin 8 - p = 0
9 Distance d from a straight line (ax + by + c = 0) to a point P(x,,y,)

ax, +by, -+ c
d=
kdPTi7
If u is the angle between ax + by + c = 0 and a'x + b'y + c' = 0 then
aa' + bb'
COSU =
kd(a2 + bZ)(a'' + b'*)

V

Figure 1-39. Equation of a straight line (normal form).