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Section 11.7 – Conics in Polar Coordinates

Section 11.7 – Conics in Polar Coordinates. E ccentricity. The ratio of the distance from a fixed point (focus) to a point on the conic to the distance from the point to the directrix is t he eccentricity of a conic. It is a constant ratio and is denoted by  e . P. D. F.

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Section 11.7 – Conics in Polar Coordinates

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  1. Section 11.7 – Conics in Polar Coordinates Eccentricity The ratio of the distance from a fixed point (focus) to a point on the conic to the distance from the point to the directrix is the eccentricity of a conic. It is a constant ratio and is denoted by e. P D F If e < 1, the conic is an ellipse.If e = 1, the conic is a parabola.If e > 1, the conic is a hyperbola.

  2. Section 11.7 – Conics in Polar Coordinates Polar Equation for a Conic with Eccentricity e The vertical directrix is represented by k. The horizontal directrix is represented by k. To use these polar equations, a focus is located at the origin.

  3. Section 11.7 – Conics in Polar Coordinates Given the eccentricity and the directrix corresponding to the focus at the origin, find the polar equation.

  4. Section 11.7 – Conics in Polar Coordinates Given the eccentricity and the directrix corresponding to the focus at the origin, find the polar equation.

  5. Section 11.7 – Conics in Polar Coordinates Polar Equation of an Ellipse with Eccentricity e and Major Axis a

  6. Section 11.7 – Conics in Polar Coordinates Given the polar equation, find the directrix that corresponds to the focus at the origin, the polar coordinates of the vertices and the center

  7. Section 11.7 – Conics in Polar Coordinates y

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