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

[JEE Main 2026, 23 Jan (Shift 2)]

Question

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

[JEE Main 2026, 23 Jan (Shift 2)]

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If the points of intersection of the ellipses \({x}^{2}+2{y}^{2}−6x−12y+23=0\) and \(4{x}^{2}+2{y}^{2}−20x−12y+35=0\) li…

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