Assertion :Any chord of the ellipse $x^{2} + y^{2} + x y = 1$ through $(0, 0)$ is bisected at $(0, 0)$ Reason: The centre of an ellipse is a point through which every chord is bisected.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$x^{2} + y^{2} + x y = 1$
Replacing $x$ by $y$ & $y$ by $x$ we get the same equation.
$∴$ Centre of conic is $(0, 0)$ and every chord passing through the centre is bisected by the point.
Hence assertion & reason both are true & assertion explains reason.

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