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Maths-

General

Easy

Question

For the ellipse $fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma$ the foci are

( ±1, 0)
(0, ± 1)
$(\pm \frac{1}{\sqrt{2}}, 0)$
$(\pm \frac{1}{2}, 0) .$

hint Hint:

To find focii, find the eccentricity by the formula
e = $square root of 1 space minus space b squared over a squared end root$

The correct answer is: ( ±1, 0)

Given : Equation of ellipse
$fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma$
Center of ellipse = (h, k) = (0,0)
Eccentricity (e) = $square root of 1 space minus space b squared over a squared end root$
$rightwards double arrow$ e = $square root of 1 space minus space 1 half end root space equals space fraction numerator 1 over denominator square root of 2 end fraction$
$rightwards double arrow$ Foci = ( h $plus-or-minus$ ae , k)
where a = $square root of 2$
$rightwards double arrow$ Foci = ( 0 $plus-or-minus$ $square root of 2 cross times fraction numerator 1 over denominator square root of 2 end fraction$ , 0)
$rightwards double arrow$ Foci = ( 0 $plus-or-minus$ $1$ , 0)
$rightwards double arrow$ Foci = ( $plus-or-minus$ $1$ , 0)

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