6.19✶✶ A surface of revolution is generated as follows: Two fixed points (x1, y₁) and (x2, y2) in the x, y plane are joined by a curve y = y(x). [Actually you'll make life easier if you start out writing this as x = x(y).] The whole curve is now rotated about the x axis to generate a surface. Show that the curve for which the area of the surface is minimum has the form y = yo cosh[(x - x)/yo], where x and yo are constants. (This is often called the soap-bubble problem, since the resulting surface is usually the shape of a soap bubble held by two coaxial rings of radii y₁ and y2.)

6.19✶✶ A surface of revolution is generated as follows: Two fixed points (x1, y₁) and (x2, y2) in the x, y plane are joined by a curve y = y(x). [Actually you'll make life easier if you start out writing this as x = x(y).] The whole curve is now rotated about the x axis to generate a surface. Show that the curve for which the area of the surface is minimum has the form y = yo cosh[(x - x)/yo], where x and yo are constants. (This is often called the soap-bubble problem, since the resulting surface is usually the shape of a soap bubble held by two coaxial rings of radii y₁ and y2.)