I'm having trouble with the last question on my AP calc homework. Can anyone show me how it's done?

Consider the curve given by $x^2 + 3y^2 = 1 + 3xy3xy$

a) show that dy/dx $\frac{dy}{dx} = 3y \frac{3y - 2x / 6y 2x}{6y - 3x3x}$

b) find all points on the curve whose x-coordinate is 1, and write an equation for the tangent line at each of these points.

c) find the coordinates of each point where the tangent line is vertical

I'm having trouble with the last question on my AP calc homework. Can anyone show me how it's done?

Consider the curve given by x^2 + 3y^2 = 1 + 3xy

a) show that dy/dx = 3y - 2x / 6y - 3x

b) find all points on the curve whose x-coordinate is 1, and write an equation for the tangent line at each of these points.

c) find the coordinates of each point where the tangent line is vertical