Conic Sections
Conic sections are curves formed by the intersection of a plane and a cone, including circles, ellipses, parabolas, and hyperbolas, each with distinct equations and properties.
What You Need to Know
Key Concept Diagram
A circle with centre (h,k) and radius r has equation (x-h)^2 + (y-k)^2 = r^2
A parabola with vertex at origin has equation y = ax^2 (vertical) or x = ay^2 (horizontal)
The focus and directrix define a parabola: every point is equidistant from both
An ellipse has two foci and the sum of distances from any point to both foci is constant
A hyperbola has two branches and the difference of distances from any point to both foci is constant
Key Vocabulary
Conic section
A curve formed by intersecting a cone with a plane
Focus
A special point used to define conic sections
Directrix
A fixed line used in the definition of a parabola
Vertex
The turning point of a parabola, or the end points of the major axis of an ellipse
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the equation of a circle with centre (2, -3) and radius 5?
Question 2
The parabola y = 3x^2 opens:
Question 3
Which conic section has the equation x^2/9 + y^2/4 = 1?
Key Concepts Summary
- ●A circle with centre (h,k) and radius r has equation (x-h)^2 + (y-k)^2 = r^2
- ●A parabola with vertex at origin has equation y = ax^2 (vertical) or x = ay^2 (horizontal)
- ●The focus and directrix define a parabola: every point is equidistant from both
- ●An ellipse has two foci and the sum of distances from any point to both foci is constant
- ●A hyperbola has two branches and the difference of distances from any point to both foci is constant