5.2 Angle Between Two Curves
Angle between two curves is the angle between two
tangents lines drawn to the two curves at their point of intersection.
If m_{1} and m_{2} are two slopes of these two tangents
and q is the acute
angle between them then we have tan q
=
Let C_{1} and C_{2} be two curves intersecting
at a point P. Then these curves are said to intersect 'orthogonally'
at P. If tangents at P to C_{1} and C_{2} are at
right angles i.e. m_{1} m_{2} = 1
Definition
Let the tangent and normal at to the curve y = f (x) meet x  axis at T and G respectively and Let PN be perpendicular to the x  axis at N. Then
(1) PT is called the "tangent length" at P
(2) PG is called the "normal length" at P
(3) The segment TN is known as the "subtangent" at P and
(4) The segment NG is known as the "subnormal" at P
Then we have
[next page]
