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

Options

A. `(y-1)(x+1)+2x=0`
B. `2x(y-1)+x+1=0`
C. `x(y-1)(x+1)+2=0`
D. None of these

Answer

A

Explanation

Slope `=(dy)/(dx)=(y-1)/x^(2)+x`
or `(dy)/(y-1)=(dx)/(x^(2)+x)`
or `int1/(y-1)dy=int(1/x-1/(x+1))dx+C` or `((y-1)(x+1))/x=k`
Putting `x=1, y=0`, we get `k=-2`.
The equation is `(y-1)(x+1)+2x=0`