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Question
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/36 + y^2/16 = 1`
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Solution
Equation of ellipse `x^2/36 + y^2/16 = 1`
Comparing with the equation `x^2/a^2 + y^2/b^2 = 1`,
a2 = 36, b2 = 16
c2 = a2 − b2
= 36 − 16
= 20
∴ c = `2sqrt5 "e" ="c"/"a"`
= `(2sqrt5)/6 = sqrt5/3`
The coordinates of the foci are (± c, 0), that is (± `2sqrt5`, 0)
vertex (± a, 0) or (± 6, 0),
Length of major axis = 2a = 2 × 6 = 12
Length of minor axis = 2b = 2 × 4 = 8
eccentricity = e = `"c"/"a" = (2sqrt5)/6 = sqrt5/3`
Length of latus rectum = `(2"b")^2/"a" = (2 xx 16)/6 = 16/3`.
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