The differential equation of all parabolas whoseaxis are parallel to the y-axis is(a)`( b ) (c) (d)(( e ) (f) d^(( g )3( h ))( i ) y)/( j )(( k ) d (l) x^(( m )3( n ))( o ))( p ) (q)=0( r )`(s)(b) `( t ) (u) (v)(( w ) (x) d^(( y )2( z ))( a a ) x)/( b b )(( c c ) d (dd) y^(( e e )2( f f ))( g g ))( h h ) (ii)=C (jj)`(kk)(c)`( d ) (e) (f)(( g ) (h) d^(( i )3( j ))( k ) y)/( l )(( m ) d (n) x^(( o )3( p ))( q ))( r ) (s)+( t )(( u ) (v) d^(( w )2( x ))( y ) x)/( z )(( a a ) d (bb) y^(( c c )2( d d ))( e e ))( f f ) (gg)=0( h h )`(ii)(d) `( j j ) (kk) (ll)(( m m ) (nn) d^(( o o )2( p p ))( q q ) y)/( r r )(( s s ) d (tt) x^(( u u )2( v v ))( w w ))( x x ) (yy)+2( z z )(( a a a ) dy)/( b b b )(( c c c ) dx)( d d d ) (eee)=C (fff)`(ggg)A. `y_(2)=2y_(1)+x`B. ` y_(3) = 2y_(1)`C. ` y_(2)^(3)=y_(1)`D. None of these

The differential equation of all parabolas whoseaxis are parallel to t

1.	The differential equation of all parabolas whoseaxis are parallel to the y-axis is(a)`( b ) (c) (d)(( e ) (f) d^(( g )3( h ))( i ) y)/( j )(( k ) d (l) x^(( m )3( n ))( o ))( p ) (q)=0( r )`(s)(b) `( t ) (u) (v)(( w ) (x) d^(( y )2( z ))( a a ) x)/( b b )(( c c ) d (dd) y^(( e e )2( f f ))( g g ))( h h ) (ii)=C (jj)`(kk)(c)`( d ) (e) (f)(( g ) (h) d^(( i )3( j ))( k ) y)/( l )(( m ) d (n) x^(( o )3( p ))( q ))( r ) (s)+( t )(( u ) (v) d^(( w )2( x ))( y ) x)/( z )(( a a ) d (bb) y^(( c c )2( d d ))( e e ))( f f ) (gg)=0( h h )`(ii)(d) `( j j ) (kk) (ll)(( m m ) (nn) d^(( o o )2( p p ))( q q ) y)/( r r )(( s s ) d (tt) x^(( u u )2( v v ))( w w ))( x x ) (yy)+2( z z )(( a a a ) dy)/( b b b )(( c c c ) dx)( d d d ) (eee)=C (fff)`(ggg)A. `y_(2)=2y_(1)+x`B. ` y_(3) = 2y_(1)`C. ` y_(2)^(3)=y_(1)`D. None of these
Answer» Correct Answer - d The equation of the family of parabolas with axis parallel to axis of Y is `(x-1)^(2) = A ( y -b)` On differenting w.r.t x, we get ` 2(x-a) = Ay_(1)` Again , on differenting w.r.t. x, we get `2 = Ay_(2)` ltbRgt And again , on differentiating w.r.t x, we get ` y _(3) = 0`