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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^2/4 + y^2/25 = 1`
Solution
Equation of ellipse `x^2/4 + y^2/25 = 1`
∴ a2 = 25, b2 = 4 or a = 5, b = 2
c2 = a2 − b2 = 25 − 4 = 21
∴ c = `sqrt21`
Coordinates of foci (± c, 0), or (0, ±`sqrt21`)
vertex coordinates (0, ± a) or (0, ± 5)
length of major axis = 2a = 2 × 5 = 10
length of minor axis = 2b = 2 × 2 = 4
eccentricity = e = `"c"/"a" = sqrt21/5`
Length of latus rectum = `(2"b"^2)/"a"`
= `(2 xx 4)/5`
= `8/5`
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