The centre of $14x^2-4xy+11y^2-44x-58y+71=0$ is :

Centre of conic is $\left(\frac{hf-bg}{ab-h^2},\frac{gh-af}{ab-h^2}\right)$ Here, $a=14,h=-2$

b = 11
g=-22
f=-29
C = 71

$\begin{array}{l}\text{ Centre }\equiv \left(\frac{(-2)(-29)-\left(11\right)(-22)}{\left(14\right)\left(11\right)-(-2{)}^2},\frac{(-22)(-2)-\left(14\right)(-29)}{\left(14\right)\left(11\right)-(-2{)}^2}\right)\\ \text{ Centre }\equiv (2,3).\end{array}$