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Find the Equation of the Circle Passing Through the Points: (5, 7), (8, 1) and (1, 3) - Mathematics

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प्रश्न

Find the equation of the circle passing through the points:

(5, 7), (8, 1) and (1, 3)

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उत्तर

Let the required circle be

\[x^2 + y^2 + 2gx + 2fy + c = 0\]  ...(1)
It passes through (5, 7), (8, 1) and (1, 3).
Substituting the coordinates of these points in equation (1):
\[74 + 10g + 14f + c = 0\] ...(2)
\[65 + 16g + 2f + c = 0\] ...(3)
\[10 + 2g + 6f + c = 0\]...(4)
Simplifying (2), (3) and (4):
\[g = \frac{- 29}{6}, f = \frac{- 19}{6}, c = \frac{56}{3}\]
Equation of the required circle:
\[x^2 + y^2 - \frac{29x}{3} - \frac{19y}{3} + \frac{56}{3} = 0\]
\[\Rightarrow\] \[3\left( x^2 + y^2 \right) - 29x - 19y + 56 = 0\]
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Advanced Concept of Circle - Standard Equation of a Circle
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पाठ 24: The circle - Exercise 24.2 [पृष्ठ ३२]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 24 The circle
Exercise 24.2 | Q 2.1 | पृष्ठ ३२

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