Tutorial 13: Geometry — Circle, Parabola, Ellipse
Tutorial problems for Session 2025/2026, Centre for Foundation Studies in Science, Universiti Malaya.
Sections
Circle (4 problems)
- Tangent and normal to a circle at a given point
- Length of tangent from an external point
- Equation of circle from diameter endpoints
- Intersection of line and circle; parallel tangents
Parabola (4 problems)
- Vertex, focus, directrix; sketching
- Equation from given conditions
- Geometric relation between parabola and circle
- Latus rectum and tangency to directrix
Ellipse (3 problems)
- Standard equation from given centre, vertex, foci
- Completing the square → standard form
- Centre at origin, finding equation from points