Let the lengths of intercepts on x –axis and y -axis made by the circle x 2 + y 2 + ax + 2 ay + c = 0, ( a < 0) be \(…

Let the lengths of intercepts on x–axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0,
(a < 0) be \(2\sqrt{2}\) and \(2\sqrt{5},\) respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to

[JEE Main 2021, 16 Mar (Shift 2)]