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Find the Equation of the Circle Passing Through the Points: (5, −8), (−2, 9) and (2, 1)

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Question

Find the equation of the circle passing through the points:

 (5, −8), (−2, 9) and (2, 1)

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Solution

Let the required circle be

\[x^2 + y^2 + 2gx + 2fy + c = 0\] ...(1)
It passes through (5, −8), (−2, 9) and (2, 1).
Substituting the coordinates of these points in equation (1):
\[89 + 10g - 16f + c = 0\] ...(2)
\[85 - 4g + 18f + c = 0\] ...(3)
\[5 + 4g + 2f + c = 0\]  ...(4)
Simplifying (2), (3) and (4):
\[g = 58, f = 24, c = - 285\]
The equation of the required circle is
\[x^2 + y^2 + 116x + 48y - 285 = 0\]
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Advanced Concept of Circle - Standard Equation of a Circle
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Chapter 24: The circle - Exercise 24.2 [Page 32]

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R.D. Sharma Mathematics [English] Class 11
Chapter 24 The circle
Exercise 24.2 | Q 2.3 | Page 32

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