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Study Guides > College Algebra

Key Concepts & Glossary

Key Concepts

  • Any conic may be determined by a single focus, the corresponding eccentricity, and the directrix. We can also define a conic in terms of a fixed point, the focus P(r,θ)P\left(r,\theta \right) at the pole, and a line, the directrix, which is perpendicular to the polar axis.
  • A conic is the set of all points e=PFPDe=\frac{PF}{PD}, where eccentricity ee is a positive real number. Each conic may be written in terms of its polar equation.
  • The polar equations of conics can be graphed.
  • Conics can be defined in terms of a focus, a directrix, and eccentricity.
  • We can use the identities r=x2+y2,x=r cos θr=\sqrt{{x}^{2}+{y}^{2}},x=r\text{ }\cos \text{ }\theta , and y=r sin θy=r\text{ }\sin \text{ }\theta to convert the equation for a conic from polar to rectangular form.

Glossary

eccentricity
the ratio of the distances from a point PP on the graph to the focus FF and to the directrix DD represented by e=PFPDe=\frac{PF}{PD}, where ee is a positive real number
polar equation
an equation of a curve in polar coordinates rr and θ\theta

Licenses & Attributions