sat suite question viewer
What is the diameter of the circle in the xy-plane with equation ?
Explanation
Choice B is correct. The standard form of an equation of a circle in the xy-plane is , where the coordinates of the center of the circle are and the length of the radius of the circle is . For the circle in the xy-plane with equation , it follows that . Taking the square root of both sides of this equation yields or . Because represents the length of the radius of the circle and this length must be positive, . Therefore, the radius of the circle is . The diameter of a circle is twice the length of the radius of the circle. Thus, yields . Therefore, the diameter of the circle is .
Choice A is incorrect. This is the radius of the circle.
Choice C is incorrect. This is the square of the radius of the circle.
Choice D is incorrect and may result from conceptual or calculation errors.