If a curve passes through the point `(2,7/2)` and has slope `(1-1/(x^(2)))` at any point (x,y) on ity , then the ordinate of the point on the curve , whose abscissa is -2, is

Options

A. `-3/2`
B. `3/2`
C. `5/2`
D. `-5/2`

Answer

a

Explanation

Given, ` (dy)/(dx) = 1- 1/(x^(2)) rArr dy (1-1/(x^(2)))dx`
`rArry = x + 1/x +C` [ on integration ]
since , the curve passing through the point `(2,7/2)`
i.e ` 7/2 = 2+1/2 + C rArr C = 1`
` :. Y = x+1/x +1 " "` …(i)
Given also `x =-2`
` :. " Ordinate " , y = -2 - 1/2 +1 = 3//2`