Q. 105.0( 4 Votes )

Find the equation

Answer :

Equation of the circle,


x2 - 6x + y2 + 12y + 15 = 0


x2 - 2(3)x + 32 + y2 + 2(6)y + 62 + 15 – 9 + 36 = 0


(x – 3)2 + (y-(-6))2 - 30 = 0


(x – 3)2 + (y-(-6))2 = (√30)2


Since, the equation of a circle having centre (h,k), having radius as "r" units, is


(x – h)2 + (y – k)2 = r2


Centre = (3,-6)


Area of inner circle = units square


Area of outer circle = units square {Given}


So,



r2 = 60


Equation of outer circle is,


(x – 3)2 + (y-(-6))2 = (√60)2


x2 - 6x + 9 + y2 - 12 y + 36 = 60


x2 - 6x + y2 +12y +45 – 60 = 0


x2 - 6x + y2 + 12y – 15 = 0


Hence, the required equation of the circle is x2 - 6x + y2 + 12y – 15 = 0.


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