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A circle on a coordinate plane is centered at the origin. It has a diameter of $8$ units. What is the equation of this circle?

${ x }^{ 2 }+{ y }^{ 2 }=16$

${ x }^{ 2 }+{ y }^{ 2 }=8$

${ x }^{ 2 }+{ y }^{ 2 }=64$

${ x }^{ 2 }+{ y }^{ 2 }=4$