Find the equation of the circle passing through the centre of the circle `x^2 + y^2 + 8x + 10 y - 7 =0` and concentric with the circle `x^2 + y^2 - 4x - 6y = 0`.

Find the equation of the circle passing through the centre of the circ

1.	Find the equation of the circle passing through the centre of the circle `x^2 + y^2 + 8x + 10 y - 7 =0` and concentric with the circle `x^2 + y^2 - 4x - 6y = 0`.
Answer» We have ` 2x ^(2) + 2y ^(2) - 8x - 12 y - 9 =0 ` `rArr x ^(2) + y ^(2) - 4x - 6y - (9)/(2) = 0 rArr x ^(2) + y ^(2) + 2gx + 2 f y + c = 0 ` ` " "` where ` g = - 2 , f =-3 and c = (-9)/(2)`. Centre of this circle ` = (-g, - f )= (2,3 )` ` therefore ` the centre of the required circle = `C(2, 3 )` Again , ` x ^(2) + y ^(2) + 2 gx + 2 fy + c = 0, ` where ` g = 4, f = 5 and c = - 7` Centre of this circle = `(-g, - f )= (- 4, - 5)`. So, the required circle passes through the point ` P(-4, - 5)`. Radius of the required circle ` = CP = sqrt (( 2+ 4 ) ^(2) + ( 3+ 5 ) ^(2)) ` `" "= sqrt ( 36 + 64 ) = sqrt (100) = 10 ` Hence, the required equation of the circle is ` (x - 2 ) ^(2) + (y - 3 ) ^(2) = (10)^(2) rArr x ^(2) + y ^(2) - 4x - 6y - 87 = 0 `

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Find the equation of the circle passing through the centre of the circle `x^2 + y^2 + 8x + 10 y - 7 =0` and concentric with the circle `x^2 + y^2 - 4x - 6y = 0`.

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