Let c and d be vectors such that | c + d |= 29 and c ×(2 i +3 j +4...

Let $\overrightarrow{\mathrm{c}} and$\overrightarrow{\mathrm{d}}$be vectors such that$|\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|=\sqrt{29}$and$\overrightarrow{\mathrm{c}} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \overrightarrow{\mathrm{d}}$. If$\lambda_{1}, \lambda_{2}$\left(\lambda_{1}>\lambda_{2}\right)$ are the possible values of $(\vec{c}+\vec{d}) \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})$, then the equation $\mathrm{K}^{2} x^{2}+\left(\mathrm{K}^{2}-5 \mathrm{~K}+\lambda_{1}\right) x y+\left(3 \mathrm{~K}+\frac{\lambda_{2}}{2}\right) y^{2}-8 x+12 y+\lambda_{2}=0$ represents a circle, for K equal to :