IP AMaths Notes (Upper Sec, Year 3-4): 07) Parabolas and Circles
Standard forms and locus techniques for conic questions in IP Additional Mathematics.
For Integrated Programme students: Your current school materials, teacher instructions, and assessment scope take precedence because IP topic sequence and depth vary by school. This is an Eclat IP guide, not the O-Level / SEC G3 exam-track guide.
How this chapter applies
- Eclat core: coordinate geometry of circles, centres, radii, intersections, and tangents form the K341-linked core; parabola work remains part of Eclat's IP route.
- School-sensitive extension: focus-directrix parabolas and implicit parabola tangents are outside K341 and should be used only where the school teaches them.
- 2027 national comparison: K341 Topic G2.4 covers circles in centre-radius and expanded form, excluding problems involving two circles.
- Check your school: confirm whether parabola focus-directrix methods or implicit differentiation are assessed.
- Exam-track route: use the separate O-Level and SEC G3 Additional Mathematics notes for K341 topic ownership.
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 07) Parabolas and Circles cover?
A: Standard forms and locus techniques for conic questions in IP Additional Mathematics.
Upper-sec AMaths emphasises the ability to flip between algebraic equations and geometric interpretations of parabolas and circles.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
New to the Integrated Programme? Start with What is IP? | Browse all free IP notes.
The core idea is simple: Parabolas and circles ask you to translate between equation and shape.
Use it as a working check: For circles, complete the square or use the centre-radius form. For parabolas, identify the vertex, opening direction, and useful tangent point.
Then go one layer deeper: Example: if a circle passes through three points, use the expanded form, substitute each point, solve for D, E, and F, then convert to centre and radius.
Choosing the conic route
Before doing algebra, identify what information is fixed: a centre, a radius, several points, a tangent point, or an equal-distance condition. That usually tells you the cleanest starting form.
