If the line ax+y=c touches both the curves x²+y²=1 and y²=4√2x, then |c| is equal to:

Tangent to y²=4√2x is y=mx+√2/m
This is also tangent to x²+y²=1 ⇒ |√2/m|/√1+m²=1 ⇒ m=±1
Tangent will be y=x+√2 or y=-x-√2
Compare with y=-ax+c ⇒ a=±1; c=±√2
∴|c|=√2