The lengths of tangent, subtangent, normal and subnormal for the curve ` y=x^(2)+x-1 ` at (1,1) are A,B,C and D respectively, then their increasing order is

Options

A. B,D,A,C
B. B,A,C,D
C. A,B,C,D
D. B,A,D,C

Answer

D

Explanation

Given `y=x^(2)+x-1`
`implies (dy)/(dx)=2x+1`
At `(1,1) (dy)/(dx)=3=m`
`:.` Length of tangent
`A=|(y_(1)sqrt(1+m^(2)))/m|=|(1sqrt(1+9))/3|=(sqrt(10))/3`
Length of subtangent `B=|(y_(1))/m|=1/3`
Length of normal
`C=|y_(1)sqrt(1+m^(2))|=|1sqrt(1+9)|=sqrt(10)`
and length of subnormal `D=|y_(1)m|=3`
Now, increasing order is B,A,D,C.