Consider the following lines
- $x-y-1=0$
- $x+y-5=0$
- $y=4$
The line 1 is the axis of the parabola, the line 2 is the tangent at the vertex to the same parabola, and the line 3 is another tangent to the same parabola at some point $P$.
Now let a circle $C$ circumscribe the triangle formed by tangent and normal at the point $P$ and the axis of the parabola.
Then how can I find the equation of the circle?
I found that the vertex of this parabola is $(3,2)$. Don't know how to proceed further.