Question

Find the length of tangent, normal, subtangent and subnormal to the curve y = x/(1 - x²) at the point having abscissa √2.

Answer 1

The perpendicular drawn from point P on x−axis meets at M(√2, 0). The subtangent is

MT = 4√2/3 - √2 = √2/3

The equation of normal is

y + √2 = - 1/3(x - √2)

which intersects x−axis at point N(-2√2, 0). The length of the normal is PN = √20 and of the subnormal is MN = 3√2.