The tangent at any point (x, y) of a curve makes an angle with the x - axis. Find the equation of the curve if it passes through (1, 2).

Find the curve for which the intercept cut – off by a tangent on the x – axis is equal to four times the ordinate of the point of contact.

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2(x + 1) = 2e^2x.

Find the equation of the curve such that the portion of the x - axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1, 2).

Find the equation to the curve satisfying and passing through (1, 0).