Mathematics · 2026
JEE Main · 23 January 2026, Shift 2 · Q10
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),…
If the points of intersection of the ellipses $\displaystyle x^2+2 y^2-6 x-12 y+23=0$ and $\displaystyle 4 x^2+2 y^2-20 x-12 y+35=0$ lie on a circle of radius $\displaystyle r$ and centre $\displaystyle (a, b)$, then the value of $\displaystyle a b+18 r^2$ is
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 55$
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JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.