Introduction to ellipses in conic form

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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. $(\frac{x-7}{5})^2 + (\frac{y+4}{3})^2=1$
2. $(\frac{x}{12})^2 + (\frac{y}{13})^2=1$

ellipse: the sum of the distances from any point on an ellipse to each focus is constant and equal to the major axis

2a

c= \sqrt{a^2 - b^2}

a

: distance from the center to a vertex

b

: distance from the center to a co-vertex

c

: distance from the center to a focus

e= \frac{c}{a}

e

: eccentricity; the larger the value of

e

, the more "squished" the ellipse

Conics - Ellipse