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Question
Find the equation of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
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Solution
Let the equation of the required circle be
The centre of the circle x2 + y2 − 6x + 12y + 15 = 0 is (3, −6).
Area of the required circle = \[2\pi r^2\]
Here, r = radius of the given circle
Now, r = \[\sqrt{9 + 36 - 15} = \sqrt{30}\]
∴ Area of the required circle = \[2\pi\left( 30 \right) = 60\pi\]
Let R be the radius of the required circle.
∴\[60\pi = \pi R^2 \Rightarrow R^2 = 60\]
Thus, the equation of the required circle is
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