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Find the Equation of the Circle Which Passes Through the Points (3, 7), (5, 5) and Has Its Centre on the Line X − 4y = 1.

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प्रश्न

Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x − 4y = 1.

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उत्तर

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, 7), (5, 5).
∴ \[58 + 6g + 14f + c = 0\] ...(2)
\[50 + 10g + 10f + c = 0\] ...(3)
The centre lies on the line x − 4y = 1.
∴\[- g + 4f - 1 = 0\]  ...(4)
Solving (2), (3) and (4):
\[g = 3, f = 1, c = - 90\]
Hence, the required equation of the circle is
\[x^2 + y^2 + 6x + 2y - 90 = 0\]
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Advanced Concept of Circle - Standard Equation of a Circle
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अध्याय 24: The circle - Exercise 24.2 [पृष्ठ ३२]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.2 | Q 4 | पृष्ठ ३२

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