Chapter 9 Quadratic Relations and Conic Sections - 9.3 Graph and Write Equations of Circles - Guided Practice for Examples 4 and 5 - Page 628: 6

$8.36$ miles

Similarly as in the example, we will be at a point on the circle $x^2+y^2=100$ with coordinate $(x,9)$. The x-coordinate will be negative. Hence: $x^2+9^2=100\\x^2=19\\x=\pm\sqrt{19}=\pm4.36$ But because $x$ is negative, $x=-4.36$. So we will be in the range from $(4,9)$ to $(-4.36,9)$, a distance of $|4-(-4.36)|=8.36$ miles