Conic Sections Introduction
Conic sections are curves formed by slicing a cone: circles, ellipses, parabolas, and hyperbolas. Each has a standard algebraic form.
What You Need to Know
Key Concept Diagram
Circle: x^2 + y^2 = r^2 (centre origin, radius r)
Parabola: y = ax^2 (opens up if a > 0, down if a < 0)
Ellipse: x^2/a^2 + y^2/b^2 = 1 (stretched circle)
Hyperbola: x^2/a^2 - y^2/b^2 = 1 (two branches opening left-right)
Key Vocabulary
Conic section
A curve formed by intersecting a plane with a double cone
Focus
A special point used in defining each conic
Vertex
The turning point of a parabola or the closest point on an ellipse to centre
Asymptote
A line that a hyperbola approaches but never touches
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Which equation represents a circle centred at the origin with radius 5?
Question 2
The equation x^2/9 + y^2/4 = 1 represents a:
Question 3
A hyperbola has the property of:
Key Concepts Summary
- ●Circle: x^2 + y^2 = r^2 (centre origin, radius r)
- ●Parabola: y = ax^2 (opens up if a > 0, down if a < 0)
- ●Ellipse: x^2/a^2 + y^2/b^2 = 1 (stretched circle)
- ●Hyperbola: x^2/a^2 - y^2/b^2 = 1 (two branches opening left-right)