15. For the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ , the right focus $\mathrm { F } ( c , 0 )$ is symmetric to point Q with respect to the line $y = \frac { b } { c } x$ , and Q lies on the ellipse. Then the eccentricity of the ellipse is $\_\_\_\_$.\\
III. Solution Questions (This section contains 5 questions, 74 points total. Solutions should include explanations, proofs, or calculation steps.)\\