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If a(x^(2)+y^(2)+2y+1)=(x-2y+3)^(2) is a...

If `a(x^(2)+y^(2)+2y+1)=(x-2y+3)^(2)` is an ellipse and `a in (b, oo)`, then the value of b is ___________

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To solve the problem, we start with the given equation: \[ a(x^2 + y^2 + 2y + 1) = (x - 2y + 3)^2 \] ### Step 1: Simplify the left side First, we can rewrite the left side of the equation: \[ x^2 + y^2 + 2y + 1 = x^2 + (y^2 + 2y + 1) = x^2 + (y + 1)^2 \] ...
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