What is the axis of symmetry of the parabola \( x=-5 y^{2}-5 \) ? Simplify any fractions. J)

The equation \( x = -5y^{2} - 5 \) is in the form of a sideways parabola, where it opens to the left. For parabolas in the form \( x = a(y - k)^{2} + h \), the axis of symmetry can be given by the vertical line \( y = k \). In this case, the equation can be rearranged to show that it is centered around \( y = 0 \), as there are no additional \( y \) terms. Therefore, the axis of symmetry for this parabola is \( y = 0 \). Now, we might be tempted to think the axis could vary - but fear not! Regardless of the "width" or "direction" of the parabola, the important part is that since there is no vertical shift, the original symmetry around the horizontal axis remains intact. So, it’s all about keeping it simple; \( y = 0 \) is the answer!