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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^2/25 + y^2/100 = 1`
Solution
Equation of ellipse `x^2/25 + y^2/100 = 1`
∴ a2 = 100, b2 = 25
∴ a = 10, b = 5
∴ c2 = a2 – b2 = 100 – 25 = 75
∴ c = `5sqrt3`
Coordinates of foci are (0, ± c) or (0, ± `5sqrt3`)
Coordinates of vertices are (0, ±a) or (0, ±10)
Length of major axis = 2a = 2 × 10 = 20
Length of minor axis = 2b = 2 × 5 = 10
Eccentricity = `e =c/a = (5sqrt3)/10 = sqrt3/2`
Length of latus rectum = `(2"b")^2/"a"`
= `(2 xx 25)/10`
= 5
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