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📈college algebra review

key term - Conic

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Definition

A conic is a curve obtained by intersecting a plane with a double-napped cone. The types of conics include ellipses, hyperbolas, and parabolas.

5 Must Know Facts For Your Next Test

  1. A circle is a special case of an ellipse where the eccentricity is zero.
  2. The standard form of an ellipse's equation is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.
  3. The standard form of a hyperbola’s equation is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ or $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$.
  4. In polar coordinates, the general equation for conics can be expressed as $r = \frac{ed}{1 + e\cos(\theta)}$ where $e$ is the eccentricity and $d$ is the directrix.
  5. The eccentricity ($e$) determines the shape of the conic: if $0 < e < 1$, it’s an ellipse; if $e = 1$, it’s a parabola; if $e > 1$, it’s a hyperbola.

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