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Question
Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.
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Solution
The centre of the circle x2 + y2 − 8x + 4y − 8 = 0 is (4, −2).
The radius of the unit circle is 1.
∴ Required equation of circle:
\[\left( x - 4 \right)^2 + \left( y + 2 \right)^2 = 1\],
\[\Rightarrow\] \[x^2 + y^2 - 8x + 4y + 19 = 0\]
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