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Conics - Ellipse

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Now Playing:Conics ellipse – Example 1a
Examples
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  1. properties of an ellipse
    Sketch each ellipse and state the:
    i) center
    ii) major axis and vertices
    iii) minor axis and co-vertices
    iv) foci
    v) eccentricity
    1. (x−75)2+(y+43)2=1(\frac{x-7}{5})^2 + (\frac{y+4}{3})^2=1

    2. (x12)2+(y13)2=1(\frac{x}{12})^2 + (\frac{y}{13})^2=1

Conics - Parabola
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Notes
ellipse: the sum of the distances from any point on an ellipse to each focus is constant and equal to the major axis 2a2a.
c=a2−b2c= \sqrt{a^2 - b^2} aa: distance from the center to a vertex
bb: distance from the center to a co-vertex
cc: distance from the center to a focus

e=cae= \frac{c}{a} ee: eccentricity; the larger the value of ee, the more "squished" the ellipse