Derivative as a Rate Measure, Tangents and Normals
5.0 Length of tangent, subtangent, normal and subnormal
5.0 Length of tangent, subtangent, normal and subnormal
Let us assume a tangent is drawn at a point $P(h,k)$ on curve $y=f(x)$ which cuts the $X$-axis at point $T$ as shown in 
figure.
figure. A normal is also drawn at the same point $P(h,k)$ on curve $y=f(x)$ which cuts the $Y$-axis at point $N$ as shown in figure.
Length of tangent is the distance between the point $P$(on which tangent is drawn) and point $T$(where tangent cuts $X$-axis).
Length of subtangent is the projection of $PT$ on $X$-axis i.e., $TM$ as shown in figure.
Length of normal is the distance between the point $P$(on which normal is drawn) and point $N$(where normal cuts the $X$-axis)
Length of subnormal is the projection of $PN$ on $X$-axis i.e., $SN$ as shown in figure.
