Question 5 AEA summer 2002:

For part (a), I did $\displaystyle -kx(2+x)=(2.5)^2-x^2$, and I got $\displaystyle (1-k)x^2-2kx-(2.5)^2=0$. I then used the quadratic formula to get $\displaystyle 4k^2-25k+25=0$, giving $\displaystyle k=5$ or $\displaystyle \frac{5}{4}$ (because if $\displaystyle f$ touches $\displaystyle g$, then $\displaystyle b^2=4ac$). However, the next step I'm confused about. Please help. What value of $\displaystyle k$ do I choose?