A contour of the magnetic potential U U\,U in a specialized laboratory setup is modeled by the curve with equation
x5y+4xy5=130 x^5 y + 4x y^5 = 130 x5y+4xy5=130Prove that the curve does not intersect the coordinate axes.
Show that
dydx=−5x4y+4y5x5+20xy4 \frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4} dxdy=−x5+20xy45x4y+4y5Prove that the curve has no stationary points.
In the case when x>0x > 0x>0, find the equation of the tangent line to the curve at the point where y=2y = 2y=2. Give your answer in the form ay+bx=cay + bx = cay+bx=c, where a,b,c a, b, c\,a,b,c are integers.
