If the points of intersection of the ellipses x^2+2y^2-6x-12y+23=0 and 4x^2+2y^2-20x-12y+35=0 lie on a circle of radius r and centre (a ,b ), then the value of ab+18r^2 is

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Correct answer: D. (d) The circle through intersection of the ellipses is S_1+ S_2=0. (1+4 )x^2+ (2+2 )y^2- (6+20 )x- (12+12 )y+ (23+35 )=0. For a circle: 1+4 =2+2 ⇒ = 12. Circle: 3x^2+3y^2-16x-18y+ 812=0 ⇒x^2+y^2- 163x-6y+ 272=0. Centre (a ,b )= ( 83 ,3 ) ,r^2= 649+9- 272= 4718. ab+18r^2= 83 3+18 4718=8+47=55.

$If the points of intersection of the ellipses x^{2} + 2 y^{2} - 6 x - 12 y + 23 = 0 and 4 x^{2} + 2 y^{2} - 20 x - 12 y + 35 = 0 lie on a circle of radius r and centre (a, b), then the value of ab + 18 r^{2} is$

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