The differential equation of the curve `x/(c-1)+y/(c+1)=1` is (a) `( b ) (c)(( d ) (e) (f)(( g ) dy)/( h )(( i ) dx)( j ) (k)-1( l ))(( m ) (n) y+x (o)(( p ) dy)/( q )(( r ) dx)( s ) (t) (u))=2( v )(( w ) dy)/( x )(( y ) dx)( z ) (aa) (bb)` (cc) (dd) `( e e ) (ff)(( g g ) (hh) (ii)(( j j ) dy)/( k k )(( l l ) dx)( m m ) (nn)+1( o o ))(( p p ) (qq) y-x (rr)(( s s ) dy)/( t t )(( u u ) dx)( v v ) (ww) (xx))=( y y )(( z z ) dy)/( a a a )(( b b b ) dx)( c c c ) (ddd) (eee)` (fff) (ggg) `( h h h ) (iii)(( j j j ) (kkk) (lll)(( m m m ) dy)/( n n n )(( o o o ) dx)( p p p ) (qqq)+1( r r r ))(( s s s ) (ttt) y-x (uuu)(( v v v ) dy)/( w w w )(( x x x ) dx)( y y y ) (zzz) (aaaa))=2( b b b b )(( c c c c ) dy)/( d d d d )(( e e e e ) dx)( f f f f ) (gggg) (hhhh)` (iiii)

Options

A. `(dy)/(dx)-1(y+x(dy)/(dx))=2(dy)/(dx)`
B. `((dy)/(dx)+1)(y-x(dy)/(dx))=(dy)/(dx)`
C. `((dy)/(dx)+1)(y-x(dy)/(dx))=2(dy)/(dx)`
D. `y^(2)//x^(2)`

Answer

C

Explanation

`x/(c-1)+y/(c+1)=1`……………(1)
or `1/(c-1)+y^(')/(c+1)=0`………….(2)
or `(y^(')-1)/(y^(')+1)=c`
Put value of c in equation (1). Thus,
`x/((y^(')-1)/(y^(')+1)-1)+y/((y^(')-1)/(y^(')+1)+1)=1`
or `(1+(dy)/(dx))(y-x(dy)/(dx))=2(dy)/(dx)`