ANSWER
[tex]x^2+y^2=100[/tex]
EXPLANATION
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h, k) = the center of the circle
r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)
The center of the circle is the origin, that is:
[tex](h,k)=(0,0)[/tex]
To find the radius, apply the formula for distance between two points:
[tex]r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}[/tex]
where (x1, y1) is the point the circle passes through
Hence, the radius is:
[tex]\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}[/tex]
Hence, the equation of the circle is:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}[/tex]
