Two tangent lines I₁ and I₂ are drawn from the point $\left(2, 0\right)$ to the parabola $2y^2=-x.$

If the lines I₁ and I₂ are also tangent to the circle ${\left(x-5\right)}^2+y^2=r$, then 17r is equal to

$$\begin{gathered} Equation of \tan gent drawn to the parabola y^2=-\frac{x}{2} is \\ y=mx-\frac{1}{8m} \\ this \tan gent pass through \left(2, 0\right) \\ \Rightarrow m=\pm \frac{1}{4} i.e., one \tan gnt is x-4y-2=0 \\ This line touches the circle {\left(x-5\right)}^2+y^2=r \\ \Rightarrow \frac{\left|5-4\left(0\right)-2\right|}{\sqrt{1+16}}=\sqrt{r} \\ 17r=9 \end{gathered}$$