The equation 2x^2 + 3y^2 - 8x - 18y + 35 = k | vedclass

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(C) Given equation: $2x^2 + 3y^2 - 8x - 18y + 35 - k = 0$.Completing the square for $x$ and $y$ terms:$2(x^2 - 4x) + 3(y^2 - 6y) + 35 - k = 0$$2(x^2 -

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$A$ point if $k = 0$

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(C) Given equation: $2x^2 + 3y^2 - 8x - 18y + 35 - k = 0$.Completing the square for $x$ and $y$ terms:$2(x^2 - 4x) + 3(y^2 - 6y) + 35 - k = 0$$2(x^2 - 4x + 4) + 3(y^2 - 6y + 9) + 35 - k - 8 - 27 = 0$$2(x - 2)^2 + 3(y - 3)^2 = k$.Case $1$: If $k = 0$,the equation becomes $2(x - 2)^2 + 3(y - 3)^2 = 0$,which represents the point $(2, 3)$.Case $2$: If $k > 0$,the equation represents an ellipse.Case $3$: If $k Thus,the correct statement is that it represents a point if $k = 0$.

The equation $2x^2 + 3y^2 - 8x - 18y + 35 = k$ represents:

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