JEE Main 2021 (Online) 17th March Morning ShiftQuestion 1
Choose the incorrect statement about the two circles whose equations are given below :
$x^{2}+y^{2}-10x-10y+41=0$ and
$x^{2}+y^{2}-16x-10y+80=0$
Circle
Solution
Circle 1: centre $(5,5)$, $r=\sqrt{25+25-41}=3$. Circle 2: centre $(8,5)$, $r=\sqrt{64+25-80}=3$. Centre distance $=3$. $0<3<6$: two intersection points (A true). Distance $=r$, so each circle passes through the other's centre (B true); average of radii $=3$ (D true). The centres lie ON, not inside, the other circle, so (C) is incorrect. Option (C).