Answer to Question #136918 in Differential Equations for K.Anushiya

Question

Find the general equation of surfaces orthogonal to the family given by
(a) x(x^2+y^2+z^2)=c1y^2
Showing that one such orthogonal set consists of the family of spheres given by
(b) x^2+y^2-z^2=c2z
If a family exists, orthogonal to both (a) and (b) show that it must satisfy
2x(x^2-z^2)dx+y(3x^2+y^2-z^2)dy+2z(2x^2+y^2)dz=0
Show that such a family in fact exists and find its equation.

Answer 1

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