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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.
16x2 + y2 = 16
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Solution
Equation of ellipse 16x2 + y2 = 16
`(16x^2)/16 + y^2/16= 1` ⇒ `x^2/1 + y^2/16= 1`
∴ The axis of the ellipse is along the y-axis.
a2 = 16, b2 = 1
∴ a = 4, b = 1
c2 = a – b2 = 16 – 1 = 15
∴ c = `sqrt15`
The coordinates of the foci are (0, ±c) or (0, ± `sqrt15`)
The coordinates of the vertices are (0, ±a) or (0, ±4)
Length of major axis = 2a = 2 × 4 = 8
Length of minor axis = 2b = 2 × 1 = 2
Eccentricity = e = `"c"/"a" = sqrt15/4`
Length of the latus rectum = `(2"b"^2)/"a"`
= `(2 xx 1)/4`
= `1/2`
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