A curve passes through the point (5,3) and the product of its slope and ordinate at any point (x,y) is equal to its abscissa. Find the equation of the curve.

A curve passes through the point (3,-4) and the slope of the tangent to the curve at any point (x,y) is (-(x)/(y)) . Find the equation of the curve.

Find the equation of the curve which passes through the point (4, 3) and the gradient of the tengent to the curve at any point on it is equal to the reciprocal of the ordinate of the point.

Find the equation of a curve passing through the point (0,1).If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate(abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

A curve passes through the point (1,(pi)/(6)) . Let, the slope of the curve at each point (x,y)" be "(y)/(x)+sec((y)/(x)),x gt0 . Then the equation of the curve is

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as (x^2-2y)/x , then the curve also passes through the point

If (dy)/(dx) = 1/x at any point (x,y) on a curve , find the equation of the family of curves

If (dy)/(dx) =2x^(2) - 3 at any point (x,y) on a curve , find the equation of the family of curves .

A circle passes through the point (-2, 1) and touches the straight line 3x - 2y = 6 at the point (4, 3) . Find its equation.

A circle passes through the points (-6, 5), (-3, -4) and its radius is 5 unit, find the equation of the circle.