ANSWER
C)
[tex] {x}^{2} + {y}^{2} = 10[/tex]
EXPLANATION
The center of the circle is (0,0).
The circle passes through (-1,-3).
The radius can be obtained using the distance formula:
[tex]r = \sqrt{(0 - 1)^{2} + {(0 - - 3)}^{2} } = \sqrt{10} [/tex]
The equation is given as:
[tex]( {x - h)}^{2} + ( {y - k)}^{2}= {r}^{2} [/tex]
Where (h,k) is the center and r is the radius.
This implies that;
[tex]( {x - 0)}^{2} + ( {y - 0)}^{2}= {( \sqrt{10)} }^{2} [/tex]
[tex] {x}^{2} + {y}^{2} = 10[/tex]
