Parabola (Geometric Definition)
Points equidistant from a focus and a directrix.
Key idea
Points equidistant from a focus and a directrix.
In depth
A parabola is all points equally far from a fixed point (the focus) and a line (the directrix). That gives the reflective property used in satellite dishes and headlights.
Worked example
For focus (0, 1) and directrix y = −1: x² = 4y.
Formula
Real-world uses
- Designing satellite dishes and car headlights that focus light or signals to one point
Common mistake
Mixing up the focus and the vertex.
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 Parabola (Geometric Definition)?
Points equidistant from a focus and a directrix. It is a topic at the expert level in Geometry.
What is the formula for Parabola (Geometric Definition)?
The key formula is y² = 4ax.
Where is Parabola (Geometric Definition) used in real life?
Real-world examples: Designing satellite dishes and car headlights that focus light or signals to one point.
What should I learn before Parabola (Geometric Definition)?
Make sure you are comfortable with Area by Coordinates (Shoelace), the previous topic in Geometry.
What is a common mistake with Parabola (Geometric Definition)?
Mixing up the focus and the vertex.
How can I practise Parabola (Geometric Definition)?
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 Parabola (Geometric Definition)?
Move on to Ellipse 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.
- Ellipse – Sum of distances to two foci is constant.
- Hyperbola – Difference of distances to two foci is constant.