you are looking for a point which produces together with point P a straight line which is perpendicular to the graph of your function. That means:
1. Q denotes the point in Question.
2. Q lies on the graph of . So if then . Therefore .
3. The derivative of p is . Therefore in point Q the graph of p has the slope m = 2a .
4. That means: The perpendicular direction is described by:
5. The straight line QP has the equation (use 2 point formula of a straight line):
6. That means: This straight line is perpendicular to the graph of the function p. Therefore: The slope of the line PQ must have the same direction as m':
Solve for a! As suggested by inspection. You should find an positive integer number.