The equation 2x^2 + 2y^2 + 4x + 8y + 15 = 0 r | vedclass

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(D) Given equation is $2x^2 + 2y^2 + 4x + 8y + 15 = 0$. Divide the entire equation by $2$: $x^2 + y^2 + 2x + 4y + \frac{15}{2} = 0$. Rearranging the t

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None of these

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(D) Given equation is $2x^2 + 2y^2 + 4x + 8y + 15 = 0$. Divide the entire equation by $2$: $x^2 + y^2 + 2x + 4y + \frac{15}{2} = 0$. Rearranging the terms to complete the square: $(x^2 + 2x + 1) + (y^2 + 4y + 4) + \frac{15}{2} - 1 - 4 = 0$. $(x + 1)^2 + (y + 2)^2 + \frac{5}{2} = 0$. $(x + 1)^2 + (y + 2)^2 = -\frac{5}{2}$. Since the sum of squares of real numbers cannot be negative,this equation does not represent any real locus (it represents an imaginary circle). Therefore,the correct option is $D$.

The equation $2x^2 + 2y^2 + 4x + 8y + 15 = 0$ represents

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