The curve is defined by $y = kx^2 + 1$ and the line is defined by $y = kx$, where $k$ is a non-zero constant.
(i)[3]
Determine the set of values of $k$ for which the curve and the line do not intersect.
(ii)[4]
State the value of $k$ for which the line is tangent to the curve and, in this case, determine the coordinates of the point at which the line touches the curve.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rearranges to the quadratic $kx^2 - kx + 1 = 0$” …