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Question
What does the equation (x − a)2 + (y − b)2 = r2 become when the axes are transferred to parallel axes through the point (a − c, b)?
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Solution
Substituting
\[x = X + a - c, y = Y + b\] in the given equation, we get:
\[\left( X + a - c - a \right)^2 + \left( Y + b - b \right)^2 = r^2 \]
\[ \Rightarrow \left( X - c \right)^2 + Y^2 = r^2 \]
\[ \Rightarrow X^2 + Y^2 - 2cX = r^2 - c^2\]
Hence, the transformed equation is
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