From the given equations, we have to find the equation which correctly represents a circle centered at a origin with a radius of 10.
Let us consider the first equation,
1. [tex] x^{2}+y^{2}=100 [/tex] can be expressed as
[tex] (x-0)^{2}+(y-0)^{2}=(10)^{2} [/tex] (Equation 1)
The general equation of sphere is [tex] (x-a)^{2}+(y-b)^{2}=(r)^{2} [/tex] 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 as (0,0) that is origin and radius is 10 units.
Therefore, it is the required equation.
2. The second equation is [tex] (x)^{2}+(y)^{2}=(100)^{2} [/tex]
By comparing this equation with general equation of sphere, we can say it is equation of sphere with center at origin but radius is 100 units.
So, it is not the required equation.
3. The third equation is [tex] (x)^{2}+(y)^{2}=(10) [/tex]
By comparing this equation with general equation of sphere, we can say it is equation of sphere with center at origin but radius is [tex] \sqrt{10} [/tex] units.
So, it is not the required equation.
4. The fourth equation is [tex] (x-10)^{2}+(y-10)^{2}=100 [/tex]
= [tex] (x-10)^{2}+(y-10)^{2}=(10)^{2} [/tex]
By comparing this equation with general equation of sphere, we can say it is equation of sphere with center at (10,10) but radius is 10 units.
So, it is not the required equation.
So, option A is the correct answer.
