The equation of the curve which is such that the portion of the axis of `x` cut off between the origin and tangent at any point is proportional to the ordinate of that point is (a) `( b ) (c) x=y(a-blogx)( d )` (e) (f) `( g ) (h)logx=b (i) y^(( j )2( k ))( l )+a (m)` (n) (o) `( p ) (q) (r) x^(( s )2( t ))( u )=y(a-blogy)( v )` (w) (d) None of these

Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1,2).

Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent art a point is twice the abscissa and which passes through the point (1,2).

The equation of the curve lying in the first quadrant, such that the portion of the x - axis cut - off between the origin and the tangent at any point P is equal to the ordinate of P, is (where, c is an arbitrary constant)

The equation of curve in which portion of y-axis cutoff between origin and tangent varies as cube of abscissa of point of contact is

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Find the curve for which the intercept cut off by any tangent on y-axis is proportional to the square of the ordinate of the point of tangency.

The equation of a curve passing through (1,0) for which the product of the abscissa of a point P and the intercept made by a normal at P on the x-axis equal twice the square of the radius vector of the point P is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=( l ) x^(( m )4( n ))( o ) (p) (q) (b) ( r ) (s) (t) x^(( u )2( v ))( w )+( x ) y^(( y )2( z ))( a a )=2( b b ) x^(( c c )4( d d ))( e e ) (ff) (gg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )+( j ) y^(( k )2( l ))( m )=4( n ) x^(( o )4( p ))( q ) (r) (s) (d) None of these

A curve is such that the intercept of the x-axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1, 2). If the ordinate of the point on the curve is 1/3 then the value of abscissa is :

Show that the area between the curve y=ce^(2x) , the x-axis and any two ordinates is proportional to the difference between the ordinates, c being constant.

The equation of the locus of the middle point of the portion of the tangent to the ellipse x^/16+y^2/9=1 included between the co-ordinate axes is the curve