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 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 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 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 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 slope of the tangent to the curve y = x^3- x at x = 2 .

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 > 0. Then the equation of the curve is

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.

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 (2,-8) and the slope of tangent at any point (x,y) is given by x^(2)/2-6x . The maximum ordinate on the curve is given by lambda then find (3lambda ).

Find the slope of tangent of the curve y =4x^2 at the point (-1,4).