First thing we do know about these curves, is that both have the point (1,0)

Let

Let

We have, when x = 1, y = 0. so for the following happens:

..............(1)

similarly, for , the following happens:

So we know the value of c, and we know one equation that relates a and b. but what else do we know?

they share a common tangent at (1,0), in particular, the slope of the tangent line at x = 1 is the same for the two curves

so, , when x = 1, we get:

and

, when x = 1, we get:

Now we equate the two slopes:

...............(2)

............since

But from equation (1),

So,