Conics - Ellipse

Conics - Ellipse

Basic concepts: Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, Pythagorean identities,

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=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
  • 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)
    (x−75)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

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10.
Conics
10.1
Conics - Parabola
10.2
Conics - Ellipse
10.3
Conics - Circle
10.4
Conics - Hyperbola
AU Maths Methods