Answer:
k = ±4
Explanation:
Equation of the circle is:
x² + y² = 5
This means from the general form of equation of a circle;
Centre coordinates is (0, 0) and radius is; √5.
The line 2x - y + k = 0 touches the circle. Thus, perpendicular distance from centre of the circle to this line is equal to the circle radius;
Thus;
|((2 - 0) - (1 × 0) + k)|/(√(2² + 1²)) = √5
|(1 + k)|/√5 = √5
Multiply both sides by √5 to get;
|1 + k| = 5
|k| = 5 - 1
k = ±4