Answer:
[tex]x^{2} + y^{2} = 100[/tex]
Step-by-step explanation:
The equation of a circle has the following format:
[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]
In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]
Centered at the origin
This means that [tex]x_{0} = 0, y_{0} = 0[/tex]
Passing through the point(0,10)
The radius is the distance of any point in which the circle passes to the centre.
Using the formula for the distance between two points.
[tex]r = D = \sqrt{(0 - 0)^{2} + (10 - 0)^{2}} = 10[/tex]
So
[tex]x^{2} + y^{2} = 10^{2}[/tex]
[tex]x^{2} + y^{2} = 100[/tex]
