मराठी

Find the Equation of the Circle Passing Through the Points: (0, 0), (−2, 1) and (−3, 2)

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प्रश्न

Find the equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)

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उत्तर

Let the required circle be

\[x^2 + y^2 + 2gx + 2fy + c = 0\]  ...(1)
It passes through (0, 0), (−2, 1) and (−3, 2).
Substituting the coordinates of these points in equation (1):
\[c = 0\] ...(2)
\[5 - 4g + 2f + c = 0\]  ...(3)
\[13 - 6g + 4f + c = 0\] ...(4)
Simplifying (2), (3) and (4):
\[g = \frac{- 3}{2}, f = \frac{- 11}{2}, c = 0\]
The equation of the required circle is
\[x^2 + y^2 - 3x - 11y = 0\]
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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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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 24 The circle
Exercise 24.2 | Q 2.4 | पृष्ठ ३२

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