[tex]\text{Given that: \: } {x}^{2} + {y}^{2} = 36[/tex]
[tex] {x}^{2} + {y}^{2} = 36 \\ \\ {y}^{2} = 36 - {x}^{2} \\ \\ y = \pm \sqrt{36 - {x}^{2} } [/tex]
[tex]\text{Thus, y as a function of x is given as:} \\ \\ \boxed{ \red{ y = f(x) = \pm \: \sqrt{36 - {x}^{2} }} }[/tex]
