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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

A

`y=x^(2)+x+1`

B

`xy=x^(2)+x+1`

C

`xy=x+1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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`
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