Final answer:
The axis of symmetry of the parabola x = -(1)/(5)y²+6 is x = 30.
Step-by-step explanation:
The equation of the parabola given is x = -1/5y² + 6. To find the axis of symmetry, we need to rewrite the equation in the form y = ax² + bx + c. Rearranging the equation, we get y² = -5x + 30. This means the parabola opens to the left and its vertex lies on the line x = 30. Since the parabola is symmetric about the axis of symmetry, the x-coordinate of the vertex is the axis of symmetry. Therefore, the axis of symmetry of the parabola x = -1/5y² + 6 is x = 30.