The slope of a curve at any point is the reciprocal of twice the ordinate at that point and it passes through the point(4,3). The equation of the curve is:

The slope of the tangent to the curve at any point is twice the ordinate at that point.The curve passes through the point (4;3). Determine its equation.

The slope of a curve, passing through (3,4) at any point is the reciprocal of twice the ordinate of that point. Show that it is parabola.

The curve y=f(x) in the first quadrant is such that the y - intercept of the tangent drawn at any point P is equal to twice the ordinate of P If y=f(x) passes through Q(2, 3) , then the equation of the curve is

The slope of normal at any point P of a curve (lying in the first quadrant) is reciprocal of twice the product of the abscissa and the ordinate of point P. Then, the equation of the curve is (where, c is an arbitrary constant)

A curve passes through the point (-2, 1) and at any point (x, y) of the curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4, -3). Find the equation of the curve.

At any point P(x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact P to the point (-4,-3) Find the equation of the curve given that it passes through the point (-2, 1)

At any point on a curve , the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point.If the curve passes through (0,1), then the equation of the curve is

A curve y=f(x) passes through point P(1,1). The normal to the curve at P is a (y-1)+(x-1)=0. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point,then the equation of the curve is