Question

Find the differential equation of the space curve in which the two families of surfaces

u = x² − y² = c₁ and

v = y² − z² = c₂ intersect.

Answer 1

$du=2xdx-2ydy=0$

$xdx=ydy$

$dv=2ydy-2zdz=0$

$ydy=zdz$

$xdx=ydy=zdz$

$\frac{xdx}{xyz}=\frac{ydy}{xyz}=\frac{zdz}{xyz}$

$\frac{dx}{yz}=\frac{dy}{xz}=\frac{dz}{xy}$

$yzp+xzq=xy$