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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.
36x2 + 4y2 = 144
Solution
Equation of ellipse 36x2 + 4y2 = 144
`(36x^2)/144 + (4y^2)/144 = 1` `x^2/4 + y^2/36 = 1`
∴ a2 = 36, b2 = 4
∴ a = 6, b = 2
∴ c2 = a2 – b2 = 36 – 4 = 32
∴ c = `4sqrt2`
The axis of the ellipse is along the y-axis
Coordinates of foci are (0, ± c) or (0, ± `4sqrt2`
Coordinates of vertices are (0, ± a) or (0, ± 6)
Length of major axis = 2a = 2 × 6 = 12
Length of minor axis = 2b = 2 × 2 = 4
Eccentricity (e) = `c/a`
= `(4sqrt2)/6`
= `(2sqrt2)/3`
Length of latus rectum = `(2"b")^2/a`
= `(2 xx 4)/6`
= `4/3`
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