Eccentricity of Conics
Measures how stretched a conic is.
Key idea
Measures how stretched a conic is.
In depth
Eccentricity e = distance to focus / distance to directrix classifies conics: e = 0 is a circle, 0 < e < 1 an ellipse, e = 1 a parabola, e > 1 a hyperbola. For an ellipse, e = c/a measures how stretched it is.
Worked example
For x²/25 + y²/9 = 1, e = 4/5 = 0.8.
Formula
Real-world uses
- Comparing how round or stretched planetary orbits are in astronomy and space mission design
Common mistake
Expecting e to be above 1 for an ellipse.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Eccentricity of Conics?
Measures how stretched a conic is. It is a topic at the expert level in Geometry.
What is the formula for Eccentricity of Conics?
The key formula is e = c/a.
Where is Eccentricity of Conics used in real life?
Real-world examples: Comparing how round or stretched planetary orbits are in astronomy and space mission design.
What should I learn before Eccentricity of Conics?
Make sure you are comfortable with Hyperbola, the previous topic in Geometry.
What is a common mistake with Eccentricity of Conics?
Expecting e to be above 1 for an ellipse.
How can I practise Eccentricity of Conics?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Eccentricity of Conics?
Move on to Compass and Straightedge next.
Related expert topics in Geometry
- Power of a Point – For a point and a circle, products of segment lengths along secants are equal.
- Cyclic Quadrilaterals – Opposite angles of a quadrilateral inscribed in a circle sum to 180°.
- Cavalieri’s Principle – Solids with equal cross-sectional areas at every height have equal volume.
- Area by Coordinates (Shoelace) – Area of a polygon from vertices.
- Parabola (Geometric Definition) – Points equidistant from a focus and a directrix.
- Ellipse – Sum of distances to two foci is constant.