Answer:
[tex]x^{2} +y^{2}=25[/tex]
Step-by-step explanation
The standard equation of a circle centered at origin is [tex]x^{2} +y^{2} =r^{2}[/tex]
r = radius of the circle
The circle is passing through the point (0,5)
∴ radius [tex]r=\sqrt{(0-0)^{2}+(5-0)^{2} }[/tex]
[tex]r=\sqrt{0+25}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r^{2}=25[/tex]
∴ The equation of the circle is
[tex]x^{2} +y^{2} = 25[/tex]
