The tangent to the curve $y=x^2+1$ at $(2,5)$ meets the normal to the curve at $(1, 2)$ 
Find the coordinates of the point where the tangent to the curve $y=x^2+1$ at the point $(2,5)$ meets the normal to the same curve at the point $(1,2).$

I tried to form 2 equations for each set of coordinates given, then solve then simultaneously to get the 'y and x' coordinates needed, however I didn't seem to get the answer right.

$y'(x) = 2x$
$y'(2) = 4$, so $4$ is the slope of the tangent at $(2,5)$.
You have a point and a slope, so you should be able to find the equation of a line.
Then $y'(1) =2$, so we invert and negate this to get the normal slope ($=-1/2$).
Point + slope --> equation.
Etc.
