Question

-\frac{x^2}{6^2} + \frac{y^2}{2^2} = 1

Explanation:

Step1: Identify the conic section type

The given equation is of the form \(-\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), which represents a vertical hyperbola.

Step2: Determine the standard equation variables

The equation has \(a = 6\) and \(b = 2\), meaning the variables must be squared.

Step3: Fill in the missing variables

Substituting \(x^2\) and \(y^2\) into the numerators yields \(-\frac{x^2}{6^2} + \frac{y^2}{2^2} = 1\).

Answer:

\(-\frac{x^2}{6^2} + \frac{y^2}{2^2} = 1\)