Cambridge AS & A Level. 2025. Mathematics (9709). May/June - Paper 1 (11) · Pure Mathematics 1 - Question 10

The equation of a curve is $2x^2 - kxy + 2 = 0$ and the equation of a line is $y = px + 3$, where $k$ and $p$ are constants.

**(a)** Given that $k = 2$ and $p = 11$, find the coordinates of the points of intersection of the curve and the line.