A wire of length 36m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then $\left(\frac{4}{\pi }+1\right)k$ $\frac{}{}$ is equal to_________.

$b^2{x}^2+a^2{y}^2=a^2{b}^2$

$\left(b^2{x}^2+a^2\left(ab-x^2\right)\right)=a^2{b}^2$

$x^2=\frac{b{a}^2\left(b-a\right)}{b^2-a^2},y^2=\frac{a{b}^2}{a+b}$

points of intersection

$\left(a\sqrt[]{\frac{b}{a+b}},b\sqrt[]{\frac{a}{a+b}}\right)$

$tan\theta =\left|\frac{m_1-m_2}{1+m_1.m_2}\right|$

$=\left|\frac{a-b}{\sqrt[]{ab}}\right|$