Tangents and Normals
P(x,y) is any point on the curve f(x,y)=c. PT is tangent at p and PN is normal at P. Angle made by tangent PT with x-axis is denoted by in anticlockwise direction.
is defined as slope of gradient of tangent PT.
We also define
= slope of tangent,
Slope of normal =
Equation of Tangent PT is
Equation of normal PN is
PM is perpendicular from P on x-axis.
Sub tangent = TM =
Sub normal = MN =
Length of Tangent = PT =
Length of normal = PN =
Where is point P.
The tangent is parallel to x-axis if:
The tangent is parallel to y –axis if:
Tangent at the origin is obtained by equating to zero the lowest degree terms, provided the curve passes through origin.
Definition of Angle of Intersection
Suppose two curves cut at P. Let be gradient of the two tangents to the two curves at the point of inserction. Angle between the two curves at P is defined as angle between the two tangents at P.
The two curves cut orthogonally if
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