Conics - Ellipse

Conics - Ellipse

Lessons

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=a2b2c= \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
  • 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
    a)
    (x75)2+(y+43)2=1(\frac{x-7}{5})^2 + (\frac{y+4}{3})^2=1

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