The equation of the circle is ![x^2+y^2=25](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25)
Explanation:
Given that the endpoints of the circle.
The coordinates of the endpoints are (5,0) and (-5,0)
<u>Center:</u>
The center of the circle can be determined using the midpoint formula,
![Center=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=Center%3D%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Substituting the diameters of the circle (5,0) and (-5,0), we get,
![Center=(\frac{5-5}{2},\frac{0-0}{2})](https://tex.z-dn.net/?f=Center%3D%28%5Cfrac%7B5-5%7D%7B2%7D%2C%5Cfrac%7B0-0%7D%7B2%7D%29)
![Center=(0,0)](https://tex.z-dn.net/?f=Center%3D%280%2C0%29)
Thus, the coordinates of the center is (0,0)
<u>Radius:</u>
The radius of the circle can be determined using the distance formula,
![r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2)
Substituting the center (0,0) and one of the endpoints (5,0), we get,
![r=\sqrt{(5-0)^2+(0-0)^2](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%285-0%29%5E2%2B%280-0%29%5E2)
![r=\sqrt{(5)^2+(0)^2](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%285%29%5E2%2B%280%29%5E2)
![r=\sqrt{25}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B25%7D)
![r=5](https://tex.z-dn.net/?f=r%3D5)
Thus, the radius of the circle is 5 units.
<u>Equation of the circle:</u>
The equation of the circle can be determined using the formula,
![(x-h)^{2}+(y-k)^{2}=r^{2}](https://tex.z-dn.net/?f=%28x-h%29%5E%7B2%7D%2B%28y-k%29%5E%7B2%7D%3Dr%5E%7B2%7D)
where center = (h,k) = (0,0) and r = 5 units
Substituting, we get,
![(x-0)^2+(y-0)^2=5^2](https://tex.z-dn.net/?f=%28x-0%29%5E2%2B%28y-0%29%5E2%3D5%5E2)
![x^2+y^2=25](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25)
Thus, the equation of the circle in standard form is ![x^2+y^2=25](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25)