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Two circle x^2+y^2=6 and x^2+y^2-6x+8=0 ...

Two circle `x^2+y^2=6` and `x^2+y^2-6x+8=0` are given. Then the equation of the circle through their points of intersection and the point (1, 1) is `x^2+y^2-6x+4=0` `x^2+y^2-3x+1=0` `x^2+y^2-4y+2=0` none of these

A

`x^(2)+y^(2)-6x+4=0`

B

`x^(2)+y^(2) - 3x + 1 =0`

C

`x^(2)+y^(2)-4y+2=0`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
The required equation of circle is , `S_(1)+lambda(S_(2)-S_(1))=0`.
`(x^(2)+y^(2)-6)+lambda(-6x+14)=0`
Also, passing through (1, 1)
`rArr -4+lambda(8)=0`
`rArr lambda=(1)/(2)`
`therefore` Required equation of circle is
`x^(2)+y^(2)-6-3x+7=0`
or `x^(2)+y^(2)-3x+1=0`
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