College Algebra CLEP Prep Practice Exam

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Which of the following is an equation for a circle?

y = x^2 – 2x + 1
x + |y| = 5
y = 2x^2 + 5
x^2 + y^2 = 25

The correct answer is: x^2 + y^2 = 25

A circle is defined by all the points that are equidistant from its center. Therefore, an equation for a circle must have both x and y terms squared and be equal to a constant. Option A is a quadratic equation and does not have both x and y terms squared. Option B is a linear equation with absolute value, which results in two line segments instead of a complete circle. Option C is also a quadratic equation but does not include a constant term, which is necessary for an equation for a circle. Thus, the equation x^2 + y^2 = 25 is the only one that fits the criteria for a circle.