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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.
4x2 + 9y2 = 36
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Solution
Equation of ellipse 4x2 + 9y2 = 36
`(4x^2)/36 + (9y^2)/36 = 1` ⇒`x^2/9 + y^2/4= 1`
The major axis is along the x-axis.
∴ a2 = 9, b2 = 4
∴ a= 3, b = 2
c2 = a2 – b2 = 9 – 4 = 5
∴ c = `sqrt5`
Coordinates of foci are (± c, 0) or (±`sqrt5`, 0)
Coordinates of vertices are (± a, 0) or (± 3,0)
Length of major axis = 2a = 2 × 3 = 6
Length of minor axis = 2b = 2 × 2 = 4
Eccentricity = e = `"c"/"a"`
= `sqrt5/3`
Length of latus rectum = `(2"b")^2/"a"`
= `(2 xx 4)/3`
= `8/3`
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