Analytical Geometry is one of 9 topics in the Grade 12 Technical Mathematics CAPS syllabus, covered across 3 lessons on Study Vault. Below are real practice questions from this topic with full worked answers.
Sample practice questions
Easy
1. What is the radius of the circle x^2 + y^2 = 36?
Answer: 6 — Since x^2 + y^2 = r^2, r^2 = 36, so r = sqrt(36) = 6.
Easy
2. Write the equation of a circle centred at the origin with radius 9.
Answer: x^2 + y^2 = 81 — Since r = 9, r^2 = 81, so the equation is x^2 + y^2 = 81.
Medium
3. For the circle x^2 + y^2 = 25, where does the point (5; 5) lie?
Outside the circle
Inside the circle
Exactly on the circle
This point cannot be tested
Answer: Outside the circle — 5^2 + 5^2 = 25 + 25 = 50, which is greater than 25, so the point lies outside the circle.
