Find the differential equations of the space curve in which the two families of surfaces #u=x^2-y^2=c_1# and #v=y^2-z^2=c_2# intersect?
1 Answer
Jul 4, 2018
# ( dx)/(yz) = ( dy)/(xz)= ( dz)/(xy)#
Explanation:
Because
#du = underbrace(2x)_(u_x)dx - underbrace(2y)_(u_y)dy = 0 qquad implies x dx = y dy qquad bbbA#
Likewise;
#dv = 2ydy - 2zdz = 0 qquad implies y dy = z dz qquad bbbB#
# ( dx)/(yz) = ( dy)/(xz)= ( dz)/(xy)#