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If L_(T')L_(N')L_(ST) and L_(SN) denote the lengths of tangent, normal sub-tangent and sub-normal, respectively, of a curve y = f(x) at a point P(2009, 2010) on it, then |
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Answer» `(L_(ST))/(2010)=(2010)/(L_(SN))` `L_(T)=|(4sqrt(1+m^(2)))/(m)|.L_(N)=|ysqrt(1+m^(2))|` where `m=(DY)/(dx)` at point `P=(x,y)` on the CURVE `y = f(x)` Now `(L_(ST))/(L_(SN))=(1)/(m^(2))=((L_(T))/(L_(N)))^(2) and L_(ST)L_(SN)=y^(2)` |
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