Question

If the centre of the circle inscribed in square formed by the lines $x^2-8x+12=0$ and $y^2-14y+45=0$ is $(a,b),$ then the value of $a+b$ is

Answer 1

We have, $x^2-8x+12=0\Rightarrow (x-6)(x-2)=0$
and, $y^2-14y+45=0\Rightarrow (y-5)(y-9)=0$
Thus, sides of square are $x=2,x=6,y=5,y=9$

$\therefore$ Centre of the circle inscribed in square is $(\frac{2+6}{2},\frac{5+9}{2})=(4,7)$
$\therefore a+b=4+7=11$