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9.12 Radius of curvature in polar form :, , Suppose the equation to a curve is given in the polar form, r= (8). Let P(r, 8) be any point on the curve. PT is, the tangent to the curve at P inclined at an angle W with, the initial line OX. @ is the angle between radius vector, OP and the tangent PT., , We know that y = 0+, , , , , , dy dO do, St nnn. 1 :, ds ds_ ds ‘ *, dé r r, Also we have tang = r— = —— = — Se, so we have tang = r qpOgy {wer Ty, dé, ie tang =—....:.(2) Differentiating (2) w.r.t 6, we get