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Find the Equation of the Circle Which Passes Through (3, −2), (−2, 0) and Has Its Centre on the Line 2x − Y = 3. - Mathematics

Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − 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 2x − 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
  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.2 | Q 3 | Page 32
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