if 2y+x+3=0 touches the circle 5X^2 + 5y^2=k

then k= ?

x²+ y² =k/5;  centre is (0,0). and radius = root(k/5).

as line touches circle so distance of line from centre equals the radius,

3/root(2²+1²)= root(k/5)

solving, k= 9