# 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

#### Answer:

# ( 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)#