The common tangent to the circles x2+y2=4 and x2+y2+6x+8y−24=0 intersects the coordinate axes at A and B respectively. If OA and OB are equal to half of the length of the major and minor axes of an ellipse respectively, where O is the origin, then the eccentricity of the ellipse is

The common tangent to the circles x2+y2=4 and x2+y2+6x+8y−24=0 inter

1.	The common tangent to the circles x2+y2=4 and x2+y2+6x+8y−24=0 intersects the coordinate axes at A and B respectively. If OA and OB are equal to half of the length of the major and minor axes of an ellipse respectively, where O is the origin, then the eccentricity of the ellipse is
Answer» The common tangent to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} + 6 x + 8 y - 24 = 0$ intersects the coordinate axes at $A$ and $B$ respectively. If $O A$ and $O B$ are equal to half of the length of the major and minor axes of an ellipse respectively, where $O$ is the origin, then the eccentricity of the ellipse is