I have differential calculus problem where I must find the coordinates of a point $C$ on a parabola. There is a point given which is $D(8,4)$ and $D$ is on a line that is intersecting with the parabola at $C.$ Also, the line where there is the point $D$ is perpendicular to the tangent of $C.$
This is the equation of the parabola:
$f(x) = -x^2+4x+2$
This is coordinates of the single point given:
$D (8,4) $
What are the coordinates of $C$?
I am having trouble with the fact that there is only point given for the intersecting line.
Thank you for helping out!