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Find the Coordinates of the Centre of the Circle Passing Through the Points P(6, –6), Q(3, –7) and R (3, 3). - Geometry

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Question

Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).

Solution

Let the centre be P(a, b)
RO = PO = QO

\[{RO}^2 = {PO}^2\]

\[\Rightarrow \left( 3 - a \right)^2 + \left( 3 - b \right)^2 = \left( 6 - a \right)^2 + \left( - 6 - b \right)^2 \]

\[ \Rightarrow 9 + a^2 - 6a + 9 + b^2 - 6b = 36 + a^2 - 12a + 36 + b^2 + 12b\]

\[ \Rightarrow 6a - 18b = 54\]

\[ \Rightarrow a - 3b = 9 . . . . . \left( 1 \right)\]

\[{PO}^2 = {OQ}^2\]

\[\left( 6 - a \right)^2 + \left( - 6 - b \right)^2 = \left( 3 - a \right)^2 + \left( - 7 - b \right)^2 \]

\[ \Rightarrow 36 + a^2 - 12a + 36 + b^2 + 12b = 9 + a^2 - 6a + 49 + b^2 + 14b\]

\[ \Rightarrow 3a + b = 7 . . . . . \left( 2 \right)\]

Multiplying (2) with 3 we get

\[a - 3b = 9 . . . . . \left( 3 \right)\]

\[9a + 3b = 21 . . . . . \left( 4 \right) \]

\[\text { Solving }\left( 3 \right) \text { and } \left( 4 \right)\]

\[a = 3, b = - 2\]

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 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 5: Co-ordinate Geometry
Problem set 5 | Q: 20 | Page no. 123
Solution Find the Coordinates of the Centre of the Circle Passing Through the Points P(6, –6), Q(3, –7) and R (3, 3). Concept: Concepts of Coordinate Geometry.
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