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Equation of a circle passing through (1...

Equation of a circle passing through (1, 2) and (2, 1) and for which line `x+y=2` is a diameter, is :

A

`x^(2)+y^(2)+2x+2y-11=0`

B

`x^(2)+y^(2)-2x-2y-1=0`

C

`x^(2)+y^(2)-2x-2y+1=0`

D

None of these

Text Solution

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The correct Answer is:
To find the equation of the circle that passes through the points (1, 2) and (2, 1) and has the line \(x + y = 2\) as a diameter, we can follow these steps: ### Step 1: Identify the center of the circle Since the line \(x + y = 2\) is a diameter, the center of the circle lies on this line. We can express the coordinates of the center \(C\) as \((a, 2 - a)\).
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