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प्रश्न
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^2/49 + y^2/36 = 1`
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उत्तर
Equation of ellipse `"x"^2/49 + "y"^2/36 = 1`
∴ a2 = 49, b2 = 36
∴ a = 7, b = 6
major axis is along the x-axis
c2 = a2 – b2 = 49 – 36 = 13
c = `sqrt13`
Coordinates of foci are (± c, 0) or `(± sqrt13, 0)`
Coordinates of vertices are (± a, 0) or (± 7, 0)
Length of major axis = 2a = 2 × 7 = 14
Length of minor axis = 2b = 2 × 6 = 12
Eccentricity = `"e" ="c"/"a" = sqrt13/7`
Length of latus rectum = `(2"b"^2)/"a"`
= `(2 xx 36)/7`
= `72/7`
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