The point also lies on the surface giving . You can now substitute this in to get .
Let L be the line y=7, x=5z. if we rotate L around the x-axis we get a surface whose equation is Ax^2+By^2+Cz^2=1
Find A, B, C
I got B=1/49 by setting x and z=0. Any hints on how to get A and C? I can show A=-25C by plugging in point (1,7,5) thinking I could get 2 equations with 2 unknowns thinking I could just use rref but all the second equation I've been able to get just says A=C=0 which is incorrect.