The eccentricity of an ellipse is a measure of how nearly circular it is. Eccentricity is defined as c/a, where c is the distance from the center to a focus and a is the distance from the center to a vertex.
a. Find the eccentricity of an ellipse with foci (±9,0) and vertices (±10,0). Sketch the graph.
b. Describe the shape of an ellipse that has an eccentricity close to 0.
`a)` set: `b^2=a^2-c^2` so equationis is:
`x^2/10^2 +y^2/(10^2-9^2)=1` `x^2/100+y^2/19=1`
`b)` `x^2/100-y^2/99=1` `e=0.1`
`c)` The ellipse in `b)` has eccentricity close to 0 and looks
and pushed on the y ass,.
`d) ` The ellipse in `a)` has eccentricity close to 1, and looks
like a cirlce ( indeed in a cirlce the ecentricity (r/r) is
equal to 1)
Sorry I slipped b^2=100xx.19=19
an shape of ellipse is not proper.
Let equation of the ellipse be `x^2/a^2+y^2/b^2=1 ,where`
`b^2=a^2(1-e^2)` ,its foci are `(+-ae,0)` and vertices are `(+-a,0),(0,+-b)` .Its centre is (0,0).
ae=9 and a=10
thus equation of the ellipse is
When eccentricity close to zero.
Almost it will looks like a circle.