4. Given the ellipse $a^{2} x^{2}+b^{2} y^{2}=5 c^{2}$ intersects with the line $a x+$ $b y=c$ at points $A$ and $B$. If $a$, $b$, and $c$ form a geometric sequence, then $\frac{b}{a}\left(k_{O A}+k_{O B}\right)=$ $\qquad$.