Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.
Identify the type of conic by inspecting squared terms and signs in the equation
Problem
What type of conic is represented by \(x^2+y^2=25\)?
Big Picture
What this problem is really about
Classify a conic by inventorying its squared-variable terms before doing any graphing. One squared variable signals one family, opposite signs on two squares signal another, and same-sign squares narrow the remaining cases. When the two positive squared coefficients are equal, the horizontal and vertical scales match; rewrite the constant as a square to check the resulting geometry.
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