Under which one of the following conditions are the lines `x= ay+b, z=cy + d` and `x=ey + f; z=gy+ h` perpendicular?

Options

A. `ae+cg-1=0`
B. `ae+bf-1=0`
C. `ae+cg+1=0`
D. `ag+ce+1=0`

Answer

C

Explanation

Given, lines x = ay + b and z = cy + d are perpendicular.
`rArr (x-b)/a=y/1=(z-d)/c …(i)`
Also,`x=ey+f and z=gy+h` are perpendicular.
`rArr (x-f)/e=y/1=(z-h)g…(ii)`
We know, for `_|_^r`line `a_1a_2+b_1b_2+c_1c_2=0`
`rArr ae +1+cg=0`