Differentiation question involving Tangent and Normal

Find the co-ordinates 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 (1,2).

I've seen the method on how to do it but I'm confused by the 'normal to the same curve' bit. If it's a normal to the same curve, wouldn't the co-ordinates be the same as that of the tangent given a tangent only passes a curve at 1 point??

Find the co-ordinates 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 (1,2).

I've seen the method on how to do it but I'm confused by the 'normal to the same curve' bit. If it's a normal to the same curve, wouldn't the co-ordinates be the same as that of the tangent given a tangent only passes a curve at 1 point??

The tangent is at the point (2,5) on the curve

The normal is at the point (1,2) on the curve.

They intersect at ??

Not sure what you mean exactly, but clearly not.

Determine the intersection point between the green and the purple line, as this is what the question is asking for.