If $(4,3)$ and $(12,5)$ are the foci of an ellipse passing through the origin, then its eccentricity is

Explanation

Distance from origin to first focus $= \sqrt{4^2 + 3^2} = 5$ Distance to second focus $= \sqrt{12^2 + 5^2} = 13$ Sum $= 18 = 2a$ Distance between foci $= \sqrt{(12-4)^2 + (5-3)^2} = 2\sqrt{17}$ Eccentricity $e = (2\sqrt{17}) / 18 = \sqrt{17}/9$