Find the points where the two curves intersect use part

Question

Consider the two curves given by x² + 2y² - 6 and x² - 4y = 0.

a. Express dy/dx in terms of x and y for both curves.

b. Find the points where the two curves intersect.

c. Use part (alpha) to find the slope of the tangent line to each curve at the points of intersection. Confirm that the tangent lines to each curve at the intersection points are perpendicular.