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The equation of the curves through the p...

The equation of the curves through the point (1, 0) and whose slope is `(y-1)/(x^2+x)` is (a) `( b ) (c)(( d ) (e) y-1( f ))(( g ) (h) x+1( i ))+2x=0( j )` (k) (l) `( m ) (n)2x(( o ) (p) y-1( q ))+x+1=0( r )` (s) (t) `( u ) (v) x(( w ) (x) y-1( y ))(( z ) (aa) x+1( b b ))+2=0( c c )` (dd) (ee)None of these

A

(y - 1) (x + 1) - 2x = 0

B

(y - 1) (x - 1) - 2x = 0

C

(y + 1) (x +1) - 2x = 0

D

(y + 1)(x-1)+ 2x = 0

Text Solution

Verified by Experts

The correct Answer is:
A
We have `(dy)/(dx) = (y - 1)/(x (x +1))` (Given)
`rArr int(dy)/(y - 1) = int(dx)/(x (x+1)) to ln |y - 1| = ln x - ln (x + 1) + C`
When x = 1, y = 0 , so 0 = 0 - ln 2 + C rArr C = ln 2
`rArr ""ln ((y-1)(x+1))/(2x) = 0 rArr ((y -1)(x +1))/(2x) = 1` to (y - 1) (x +1) - 2x = 0`
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