What is the Difference Between Parabola and Hyperbola?
🆚 Go to Comparative Table 🆚The main difference between a parabola and a hyperbola is their eccentricity, which is a measure of the shape of a conic section. Here are the key differences between parabolas and hyperbolas:
- Eccentricity: A parabola has an eccentricity of 1, while a hyperbola has an eccentricity greater than 1.
- Focus and Directrix: A parabola has a single focus and a single directrix, while a hyperbola has two foci and two directrices.
- Shape: All parabolas have the same shape irrespective of size, while hyperbolas can have different shapes.
- The Two Arms: In a parabola, the two arms are parallel to each other, while in a hyperbola, the arms open in opposite directions.
In summary, while both parabolas and hyperbolas are conic sections, they differ in their eccentricity, focus, directrix, and shape. A parabola has a single focus and directrix, an eccentricity of 1, and a consistent shape, with two arms that are parallel. In contrast, a hyperbola has two foci and directrices, an eccentricity greater than 1, and varying shapes, with two arms that open in opposite directions.
Comparative Table: Parabola vs Hyperbola
The main difference between a parabola and a hyperbola is their eccentricity, which is equal to 1 for a parabola and greater than 1 for a hyperbola. Here is a comparison table highlighting the differences between a parabola and a hyperbola:
Feature | Parabola | Hyperbola |
---|---|---|
Definition | Set of points equidistant from a single focus and a directrix | Set of points with the difference of distances to two fixed points as a positive constant |
Focus | Single focus | Two foci |
Directrix | Single directrix | Two directrices |
Eccentricity | E = 1 | E > 1 |
Shape | Symmetrical U-shape, extends infinitely | Can be different shapes, two distinct branches never intersect |
Equation | y^2 = 4ax (standard form) | x^2/a^2 - y^2/b^2 = 1 (standard form) |
Asymptotes | None | Two asymptotes |
A parabola has a single focus and directrix, and its shape is symmetric, while a hyperbola has two foci and directrices, and its shape can vary. Additionally, a parabola extends infinitely, whereas a hyperbola has two distinct branches that never intersect.
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