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

Find the equation of the curve passing through the point (0,-2) given that at any point (x,y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x-coordinate of the point.

Find the equation of a curve passing through the point (0," "2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

If a curve passes through the point (2,7/2) and has slope (1-1/(x^(2))) at any point (x,y) on ity , then the ordinate of the point on the curve , whose abscissa is -2, is

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.

Find the equation of a curve such that the projection of its ordinate upon the normal is equal to its abscissa.

Find the equation of a curve such that the projection of its ordinate upon the normal is equal to its abscissa.

Find the equation of the curve passing through the point (0,0) and whose slope of the normal at a point (x, y) is equal to the sum of the ordinate and the product of the abscissa and 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.