What are the characteristics of the circle function with equation x^2 + y^2 = r^2? Provide a detailed explanation including its center, radius, and properties related to symmetry, intercepts, and graph shape.
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Find the equation of an ellipse with a center at (3, -2), x-intercepts (-1, 0) and (7, 0), and a major axis length of 12.
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What is the limit as x approaches 0 of (5x + 8)/(2x - 3)?