Solve {l}{(4k)^{2}+b^2=4R^2quadb=(11/6+R)k}{2R=bkquad(11/6+R)^2+16=b^2}

$$\left. \begin{array} { l } { ( 4 k ) ^ { 2 } + b ^ { 2 } = 4 R ^ { 2 } \quad b = ( 1 \frac { 1 } { 6 } + R ) k } \\ { 2 R = b k \quad ( 1 \frac { 1 } { 6 } + R ) ^ { 2 } + 16 = b ^ { 2 } } \end{array} \right.$$

Solve for k, b, R (complex solution)

$$k=\frac{i\sqrt{b}\sqrt{b-4R^{2}}}{4}\text{, }b\in \mathrm{C}\text{, }R\in \mathrm{C}$$

$$k=-\frac{i\sqrt{b}\sqrt{b-4R^{2}}}{4}\text{, }b\in \mathrm{C}\text{, }R\in \mathrm{C}$$

Solve for k, b, R

$$k=0\text{, }b=0$$

$$k=-\frac{\sqrt{b\left(4R^{2}-b\right)}}{4}\text{, }b\in \begin{bmatrix}0,4R^{2}\end{bmatrix}\text{, }R\neq 0\text{; }k=\frac{\sqrt{b\left(4R^{2}-b\right)}}{4}\text{, }b\in \begin{bmatrix}0,4R^{2}\end{bmatrix}\text{, }R\neq 0$$