Maths-
General
Easy
Question
For the ellipse
the foci are
- ( ±1, 0)
- (0, ± 1)
Hint:
To find focii, find the eccentricity by the formula
e = ![square root of 1 space minus space b squared over a squared end root](data:image/png;base64,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)
The correct answer is: ( ±1, 0)
Given : Equation of ellipse
![fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma](data:image/png;base64,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)
Center of ellipse = (h, k) = (0,0)
Eccentricity (e) =![square root of 1 space minus space b squared over a squared end root](data:image/png;base64,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)
e =![square root of 1 space minus space 1 half end root space equals space fraction numerator 1 over denominator square root of 2 end fraction](data:image/png;base64,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)
Foci = ( h
ae , k)
where a = ![square root of 2](data:image/png;base64,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)
Foci = ( 0
, 0)
Foci = ( 0
, 0)
Foci = (
, 0)
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