Final answer:
To reduce the equation 15x² - y + 5z² = 0 to one of the standard forms, we first rearrange it to isolate 'y', giving y = 15x² + 5z². Without further context, we cannot simplify this equation to a more recognized standard form or conic section.
Step-by-step explanation:
The student has provided the equation 15x² - y + 5z² = 0, which they need to reduce to one of the standard forms. First, we rearrange the equation to isolate the variable 'y':
y = 15x² + 5z²
This still may not look like one of the standard forms one might recognize, such as something comparable to the general form of a second-degree polynomial ax² + bx + c. If we consider the equation as a conic section, for example, we still need additional context or constraints to simplify further or to classify. As such, without additional information regarding what the 'standard forms' refer to in this context, we cannot definitively reduce this equation further.