The equation of a curve is $$\(y=\frac{1}{2} k^{2} x^{2}-2 k x+2\)$$ and the equation of a line is $$\(y=k x+p\)$$, where $$\(k\)$$ and $$\(p\)$$ are constants with $$\(0< k< 1\)$$. It is given that one of the points of intersection of the curve and the line has coordinates $$\(\left(\frac{5}{2}, \frac{1}{2}\right)\)$$. Find the values of $$\(k\)$$ and $$\(p\)$$, and find the coordinates of the other point of intersection. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . DO NOT WRITE IN THIS MARGIN ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

Answer:

Knowledge points:

Solution: