Compute the area of the circle that passes through all the intersection points of $4x^2 + 11y^2 = 29$ and $x^2 - 6y^2 = 6.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute the area of the circle that passes through all the intersection points of $4x^2 + 11y^2 = 29$ and $x^2 - 6y^2 = 6.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7 \pi
Compute the area of the circle that passes through all the intersection points of $4x^2 + 11y^2 = 29$ and $x^2 - 6y^2 = 6.$
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