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Prove that the equation x^(2)+y^(2)-2x-2...

Prove that the equation `x^(2)+y^(2)-2x-2ay-8=0, a in R ` represents the family of circles passing through two fixed points on x-axis.

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To prove that the equation \( x^2 + y^2 - 2x - 2ay - 8 = 0 \) represents a family of circles passing through two fixed points on the x-axis, we can follow these steps: ### Step 1: Rewrite the equation We start with the given equation: \[ x^2 + y^2 - 2x - 2ay - 8 = 0 \] We can rearrange this equation to isolate the terms involving \( y \): ...
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