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Find the Equation of the Circle Which Touches the Axes and Whose Centre Lies on X − 2y = 3. - Mathematics

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 =

\[\left( x - 1 \right)^2 + \left( y + 1 \right)^2 = 1\]
=\[x^2 + y^2 - 2x + 2y + 1 = 0\]
Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.1 | Q 9 | Page 21
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