Find the tangent to the Folium of Descartes

Question

x^3+y^3=6xy at the point (3,3)?

Answer 1

Calculate the tangent of the x^3+y^3=6xy

Take derivative bothsides

3x^2+3y^2dy/dx =6xdy/dx+6y

(3y^2-6x)dy/dx=(6y-3x^2)

dy/dx=(6y-3x^2)/(3y^2-6x)

At (3,3)

dy/dx=(6(3)-3(3)^2)/(3(3)^2-6(3))

        =(18-27)/27-18

       =-1

Slope of the tangent line , m =-1

Point, (3,3)

Find the tangent equation by using the point slope form:

y-y1 = m (x-x1)

y-3=-1(x-3)

y-3=-x+3

x+y=6