For parabola $x^{2} + y^{2} + 2 x y - 6 x - 2 y + 3 = 0$ , the focus is

(1, - 1)

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(- 1, 1)

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(3, 1)

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n o n e o f t h e s e

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Solution

The correct option is D $n o n e o f t h e s e$
From given equation, we get equation of parabola as
${(x + y - 3)}^{2} = - 4 (y - \frac{3}{2})$
Then center of parabola is $(\frac{3}{2}, \frac{3}{2})$
And distance of focus from it is $1$ unit in negative direction.
Then we get focus as $(\frac{1}{2}, \frac{3}{2})$ .

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