What is the difference between ellipse, parabola, and hyperbola in conic sections?
Answer (1)
| Features | Ellipse | Parabola | Hyperbola |
| Definition | A set of points where the sum of the distances from two fixed foci is constant. | A set of points equidistant from a fixed point called the focus and a fixed line called the directrix. | A set of points where the absolute difference of distances from two fixed foci is constant. |
| Shape | Oval shaped | U-shaped | Two separate open curves(Look like two infinite bows) |
| Standard Equation | $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ | $y^2=4 a x$ | $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ |
| Foci | $( \pm c, 0) \text {, where } c^2=a^2-b^2$ | $(a, 0)$ | $( \pm c, 0) \text {, where } c^2=a^2+b^2$ |
| Eccentricity (e) | $0<e<1$ | $e=1$ | $e>1$ |
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