The equation of a curve passing through `(2,7/2)` and having gradient `1-1/(x^2)` at `(x , y)` is (a) `( b ) (c) y=( d ) x^(( e )2( f ))( g )+x+1( h )` (i) (b) `( j ) (k) x y=( l ) x^(( m )2( n ))( o )+x+1( p )` (q) (c) `( d ) (e) x y=x+1( f )` (g) (d) None of these

Options

A. `y=x^(2)+x+1`
B. `xy=x^(2)+x+1`
C. `xy=x+1`
D. None of these

Answer

B

Explanation

We have `(dy)/(dx)=1-1/x^(2)` or `y=x+1/x+C`
This passes through `(2,7//2)`
Therefore, `7/2=2+1/2+C` or `C=1`
Thus, the equation of the curve is
`y=x+1/x+1` or `xy=x^(2)+x+1`