so I have this question here.
''We say two curves are tangent to each other at a point $P$, if both of these curves pass through $P$ and have the same tangent line at $P$. Find $a$, $b$ and $c$ (if any) such that the curves $y=x^2+ax+b$ and $y=cx-x^2$ are tangent to each other at the point $(1,0)$.''
First of all, what is this even asking? The curves should be tangent to each other right? Does that mean both curves should touch each other a exactly one point?
Second, how would I go about doing this? I have a good idea but I am not sure if it's right. The tangent line slopes should be equal to each other so I was going to take the derivative and set them equal to each other.
The problem is that I don't know if $(1,0)$ are common to both curves so I can't plug those values in to get some sort of system of equations.
Any guidance on this?