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The equation of circle concentric with c...

The equation of circle concentric with circle `x^2+y^2-6x+ 12y+ 15=0` and double its area is

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Given equation of the circle is
`x^(2)+y^(2)-6x+12y+15=0`
`therefore2g=-6rArrg=-3`
and `2f=12` `rArr` `f=6`
`C=15`
Centre `=(-g,-f)=(3,-6)`
So, the centre of the required circle will be `(3,-6),` [since, the circles are concentric]
Radius of the given circle
`=sqrt(g^(2)+f^(2)-c)`
`=sqrt(9+36-15)=sqrt(30)`
Let radius of the required circle=`r_(1)`
`therefore2xx`Area of the given circle=Area of the required circle
`rArr2[pi(sqrt(30))^(2)]=pir_(1)^(2)`
`rArr60=r_(1)^(2)`
`rArrr_(1)=sqrt(60)`
`therefore sqrt(g^(2)+f^(2)-c)=sqrt(60)`
`rArr 9+36-c=60`
`rArrc=-15`
So, the required equation of circle is `x^(2)+y^(2)-6x+12y-15=0`
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