Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The curve is described by $y = \frac{1}{2}kx^2 - 2kx + 2$, whereas the line is given by $y = kx + p$; here $k$ and $p$ are constants with $0 \le k \le 1$.
(a)[7]
It is also given that one of the intersections of the curve and the line is at $\left(\frac{5}{2}, \frac{1}{2}\right)$. Determine the values of $k$ and $p$, and then determine the coordinates of the other intersection point.
(b)[3]
Instead, suppose that the line and the curve do not meet. Find the set of possible values of $p$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set the curve equal to the line to obtain a quadratic equation” …