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Question

The centre of the circle cutting x2+y2−2x+4y−1=0 orthogonally and passing through (0, 0) , (2,0) is

A
(32,1)
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B
(1,34)
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C
(1,34)
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D
(1,3)
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Solution

The correct option is A (1,34)
Let, S:x2+y2+2gx+2fy=0 be the equation of the circle passing through (0,0) and (2,0)
The two circles are orthogonal to each other. Hence,
2g1g2+2f1f2=c1+c2
2g(1)+2f(2)=01
4f2g=1 --------(1)
The point (2,0) lies on the circle. Hence,
4+4g=0
g=1
f=34
So, centre of circle is (g,f)=(1,34)
Hence, option 'B' is correct.

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