Question

Find the implicit equation of the curve that goes through the point (3,1) and whose tangent and normal lines always form with the x-axis a triangle whose area is equal to the slope of the tangent line. Assume y' > 0 and y > 0 and using the hint that {Int}(sqrt(a^2 - u^2)/u)du = sqrt(a^2 - u^2) - a*ln((a + sqrt(a^2 - u^2))/u) + c