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Question
Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.
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Solution
If the circle lies in the third quadrant, then its centre will be (−a, −a).
The centre lies on x − 2y = 3.
∴\[- a + 2a = 3 \Rightarrow a = 3\]
∴ Required equation of the circle = \[\left( x + 3 \right)^2 + \left( y + 3 \right)^2 = 9\]
=\[x^2 + y^2 + 6x + 6y + 9 = 0\]
If the circle lies in the fourth quadrant, then its centre will be (a, −a),
∴\[a + 2a = 3 \Rightarrow a = 1\]
∴ Required equation of the circle =
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