Find the equation of the cure which passes through the origin and has the slope `x+3y-1\ ` at the point `(x , y)` on it.

Find the equation of the curve which passes through the point (3,-4) and has the slope (2y)/x at any point (x , y) on it.

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.

Find the equation of the circle which passes through the points (3,7), (5,5) and has its centre on the line x-4y=1.

Find the equation of the curve which passes through (1,0) and the slope of whose tangent at (x,y) is (x^2+y^2)/(2xy)

Find the equation of the curve passing through the point (1,0) if the slope of the tangent to the curve at any point (x ,y)i s(y-1)/(x^2+x)dot

Find the equation of the circle which passes through the points (3, -2), (-2, 0) and has its centre on the line 2x - y =3.

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 equations of the circles which pass through the origin and cut off chords of length a from each of the lines y=x and y=-x

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.