So here is my assignment for the night and I could use some direction. Suppose N =(n, n^2) and P = (p,p^2) are two points on the graph of a parabola

So here is my assignment for the night and I could use some direction.

Suppose N =(n, n^2) and P = (p,p^2) are two points on the graph of a parabola such that the tangent lines to the parabola through P and N are perpendicular. Let D be the point where the tangent lines meet at a right angle. Find the x and y coordinates of point D in terms of n.

I can find the equation for the tangent lines for P and N but then am struggling getting the coordinates in terms of n. I assume you set the two eauations equal to each other and solve for the x, and then substitute back to get the y coordinate. But I cannot seem to get it to work. Any help with work I can see and follow?