In the xy -plane, the graph of is a circle. What is the radius of the circle?

Question

Accepted Answer

Choice A is correct. One way to find the radius of the circle is to rewrite the given equation in standard form, , where is the center of the circle and the radius of the circle is r . To do this, divide the original equation, , by 2 to make the leading coefficients of and each equal to 1: . Then complete the square to put the equation in standard form. To do so, first rewrite as . Second, add 2.25 and 0.25 to both sides of the equation: . Since , , and , it follows that . Therefore, the radius of the circle is 5. Choices B, C, and D are incorrect and may be the result of errors in manipulating the equation or of a misconception about the standard form of the equation of a circle in the xy -plane.

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