An Ellipse in Disguise

★ 6/10Completing the Square conic sections analytic geometry

Problem

In the coordinate plane, the equation

m\left(x^2 + y^2 + 2y + 1\right) = (x - 2y + 3)^2

describes an ellipse. Find the range of possible values of $m$ .

Answer

Solution

Difficulty	6/10
Topics	Completing the Square, conic sections, analytic geometry

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