General Idea:
[tex]Equation \; of \; the \; circle \; is \; given \; by:\\(x-h)^2+(y-k)^2=r^2\\Where:\\(h,k) \; is \; the \; centre\\r \; is \; the \; radius[/tex]
Applying the concept :
[tex]Given \; Center \; of \; the \; circle \; at \; the \; origin,\\So \; (h, k)=(0,0)\\\\Circle \; passing \; through \; (3,-5)\\So \; Radius \; is \; the \; distance \; between \; (0, 0) \& (3,-5)[/tex]
[tex]R=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\Substituting \; (0,0) \; \& \; (3,-5)\\\\R=\sqrt{(-5-0)^2+(3-0)^2}=\sqrt{25+9}=\sqrt{34}[/tex]
Conclusion:
By substituting the above information the equation of circle, we get...
[tex](x-0)^2+(y-0)^2=(\sqrt{34})^2\\(x-0)^2+(y-0)^2=34[/tex]
