Hello, I ran across this problem and want to make sure my answers are right.

Consider the curve defined by

x^2 + xy + y^2 = 27.

a. Write an expression for the slope of the curve at any point (x,y).

b. Determine whether the lines tangent to the curve at the x-intercepts of the curve are parallel. Show the analysis that leadds to your conclusion.

c. Find the points on the curve where the lines tangent to the curve are vertical.

Thanks for your help!