Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2*x* − *y* = 3.

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#### Solution

Let the required equation of the circle be

\[x^2 + y^2 + 2gx + 2fy + c = 0\] ...(1)

It is given that the circle passes through (3, −2), (−2, 0).

∴ \[13 + 6g - 4f + c = 0\]...(2)

\[4 - 4g + c = 0\] ...(3)

The centre lies on the line 2

*x*−*y*= 3.∴\[- 2g + f - 3 = 0\] ...(4)

Solving (2), (3) and (4):

\[g = \frac{3}{2}, f = 6, c = 2\]

Hence, the required equation of circle is

\[x^2 + y^2 + 3x + 12y + 2 = 0\]

Concept: Circle - Standard Equation of a Circle

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