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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^2/16 + y^2/9 = 1`
Solution
Equation of ellipse `x^2/16 + y^2/9 = 1`
a2 = 16, b2 = 9 i.e. a = 4, b = 3
c2 = a2 − b2
= 16 − 9
= 7
∴ c = `sqrt7`
The coordinates of the foci are (± c, 0) or (± `sqrt7`, 0)
vertex coordinates (± a, 0) या (± 4, 0)
Length of major axis = 2a = 2 × 4 = 8
Length of minor axis = 2b = 2 × 3 = 6
Eccentricity = e = `c/a = sqrt7/4`
Length of latus rectum = `(2b)^2/2 = (2 xx 9)/4 = 9/2`.
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