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# Which of the following equations correctly represents a circle centered at the origin with a radius of 10? A. x2 + y2 = 100 B. x2 + y2 = 1002 C. x2 + y2 = 10 D. (x - 10)2 + (y - 10)2 = 100

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Of the equations, we have to find the equation that correctly represents a circle centered at the origin with a radius of 10.Consider the first equation,1. can be expressed as (Equation 1)The general equation of the sphere is where (a,b) is the center and r is the radius of the sphere. (Equation 2)Comparing equation 1 with equation 2 so, we get center (0,0) is the origin and the radius is 10 units.Therefore, it is necessary equation.2. The second equation isBy comparing this equation with the general equation of a sphere, we can say that it is the equation of the sphere with center at the origin, but the radius is 100 units.Thus, it is not the required equation.3. The third equation is by comparing this equation with the general equation of a sphere, we can say that it is the equation of the sphere with center at the origin, but the radius is units.Thus, it is not the required equation.4. The fourth equation is= comparing this equation with the general equation of a sphere, we can say that it is the equation of the sphere with center in (10,10) but the radius is 10 units.Thus, it is not the required equation.So, option a is the correct answer.