The equation x^2 - 4y^2 - 2x + 16y - 40 = 0 r | vedclass

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(C) Given equation: $x^2 - 4y^2 - 2x + 16y - 40 = 0$Rearranging the terms:$(x^2 - 2x) - 4(y^2 - 4y) = 40$Completing the square:$(x^2 - 2x + 1) - 4(y^2

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$A$ hyperbola

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(C) Given equation: $x^2 - 4y^2 - 2x + 16y - 40 = 0$Rearranging the terms:$(x^2 - 2x) - 4(y^2 - 4y) = 40$Completing the square:$(x^2 - 2x + 1) - 4(y^2 - 4y + 4) = 40 + 1 - 16$$(x - 1)^2 - 4(y - 2)^2 = 25$Dividing by $25$:$\frac{(x - 1)^2}{25} - \frac{(y - 2)^2}{25/4} = 1$This is of the form $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$,which represents a hyperbola.

The equation $x^2 - 4y^2 - 2x + 16y - 40 = 0$ represents:

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