A curve C has parametric equations x = 3cos(t) + 2, y = 4sin(t) - 1, for 0 ≤ t < 2π. (b) Hence, sketch the curve C, clearly indicating the coordinates of any points where the curve meets the coordinate axes.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. B1 for correctly identifying the shape as an ellipse.
2. M1 for attempting to find the intercepts by setting x=0 or y=0.
3. A1 for correct y-intercepts (y = -1 ± √12 or -1 ± 2√3) OR correct x-intercepts (x = 2 ± 9/4 or 2 ± 2.25). (Accept exact values or decimal approximations for these marks)
4. A1 for a correct sketch with all intercepts (or major/minor axes endpoints) correctly labelled. The ellipse must be centered at (2, -1).