Mathematics - Circle Question with Solution | TestHub

Let $\vec{r}$ be the position vector of a point in the Cartesian $OXY$ plane such that $\vec{r}\cdot (10\hat{j}-8\hat{i}-\vec{r})=40$, $\max \left\{|\vec{r}+2\hat{i}-3\hat{j}{|}^2\right\}=l$ and $\min \left\{|\vec{r}+2\hat{i}-3\hat{j}{|}^2\right\}=m$. A tangent line is drawn to the curve $y=\frac{8}{x^2}$ at the point $A$ with abscissa 2. The tangent cuts the $x$-axis at $B.l+m$ is equal to