The curve $C$ is given by the equation

The line $y=x$ intersects with $C$ at the point $A$.

Find the equation of the normal to $C$ at $A$, giving your answer in the form

where $a>0$ and $a,b,c$ are coprime.

To find $A$, substitute $y=x$ into the equation of $C$ and solve.

When differentiating the right hand side, you need to use the chain rule followed by the product rule when differentiating $xy$.

Give the value of $123abc$