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Question
Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
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Solution
The equation of the required circle is \[\left( x - 1 \right)^2 + \left( y - 2 \right)^2 = a^2\].
The circle passes through (−2, 6).
∴ \[\left( - 2 - 1 \right)^2 + \left( 6 - 2 \right)^2 = a^2\]
\[\Rightarrow 9 + 16 = a^2 \]
\[ \Rightarrow a = 5\]
∴ Area of the required circle = \[\pi a^2 = \pi \left( 5 \right)^2 = 25\pi \text { square units .}\]
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