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Shift the origin to a suitable point so ...

Shift the origin to a suitable point so that the equation `y^2+4y+8x-2=0` will not contain a term in `y` and the constant term.

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To solve the problem of shifting the origin to a suitable point so that the equation \( y^2 + 4y + 8x - 2 = 0 \) does not contain a term in \( y \) and the constant term, we can follow these steps: ### Step 1: Shift the Origin Let’s assume we shift the origin to a point \( (h, k) \). This means we will replace \( x \) and \( y \) in the equation with \( x' = x + h \) and \( y' = y + k \). ### Step 2: Substitute the New Variables Substituting \( x \) and \( y \) into the equation: \[ ...
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