If the points of intersection of the ellipses and lie on a circle of radius and centre

MATHEMATICS · Numerical · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the points of intersection of the ellipses x2+2y2−6x−12y+23=0x^2+2y^2-6x-12y+23=0 and 4x2+2y2−20x−12y+35=04x^2+2y^2-20x-12y+35=0 lie on a circle of radius rr and centre (a,b)(a,b), find ab+18r2ab+18r^2.

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