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 m1 and m2 are two slopes of these two tangents
and q is the acute
angle between them then we have tan q
Let C1 and C2 be two curves intersecting
at a point P. Then these curves are said to intersect 'orthogonally'
at P. If tangents at P to C1 and C2 are at
right angles i.e. m1 m2 = -1
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 "sub-tangent" at P and
(4) The segment NG is known as the "sub-normal" at P
Then we have