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

Links