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Find the equation of the circle having (...

Find the equation of the circle having `(1,-2)` as its centre and passing through the intersection of the lines `3x+y=14` and `2x+5y=18.`

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Given that, centre of the circle is `(1,-2)` and the circle passing through the lines
`3x+y= 14`….(i)
and `2x+5y=18`…(ii)
From Eq. (i) `y=14-3x` pu in Eq. (ii), we get
`2x+70-15x=18`
`rArr` `-13x=-52` `rArr` `x=4`
Now, `x=4` put in Eq. (i) we get
`12+y=14 ` `rArr` `= y = 2`
Since, point `(4, 2)` lie on these lines also lies on the circle.
Radius of the circle =`sqrt((4-1)^(2)+(2+2)^(2))`
`=sqrt(9+16)=5`
Now equation of the circle is
`(x-1)^(2)+(y+2)^(2)=5^(2)`
`rArr x^(2)-2x+1+y^(2)+4y+4=25`
`rArr x^(2)+y^(2)-2x+4y-20=0`
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