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प्रश्न
Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci
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उत्तर
Let the equation of the ellipse be
`x^2/"a"^2 + y^2/"b"^2` = 1
It is given that,
distance between directrices is three times the distance between the foci.
∴ `(2"a")/"e"` = 3(2ae)
∴ 1 = 3e2
∴ e2 = `1/3`
∴ e = `1/sqrt(3)`. ...[∵ 0 < e < 1]
संबंधित प्रश्न
Answer the following:
Find the
- lengths of the principal axes
- co-ordinates of the foci
- equations of directrices
- length of the latus rectum
- distance between foci
- distance between directrices of the ellipse:
`x^2/25 + y^2/9` = 1
Find the
- lengths of the principal axes.
- co-ordinates of the focii
- equations of directrics
- length of the latus rectum
- distance between focii
- distance between directrices of the ellipse:
3x2 + 4y2 = 12
Find the
- lengths of the principal axes.
- co-ordinates of the focii
- equations of directrics
- length of the latus rectum
- distance between focii
- distance between directrices of the ellipse:
2x2 + 6y2 = 6
Find the
- lengths of the principal axes.
- co-ordinates of the focii
- equations of directrices
- length of the latus rectum
- distance between focii
- distance between directrices of the ellipse:
3x2 + 4y2 = 1
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