Final answer:
To find the asymptotes of a vertical hyperbola, one should use a standard form equation for a vertical hyperbola, \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\), and the slopes of the asymptotes are \(\pm\frac{a}{b}\). If only \(a\) is given, one typically needs to find \(b\) using additional information about the hyperbola, but given \(a\) and \(b\), asymptotes can be found through the equations \(y = \pm\frac{a}{b}x\). The \(c\) value mentioned could be from a totally different context, such as a term in a quadratic equation.
Step-by-step explanation:
To find the asymptotes of a vertical hyperbola, you first need to understand that the equation of a hyperbola in standard form is
- For a vertical hyperbola centered at the origin: \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)
- For a horizontal hyperbola centered at the origin: \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\)
If the hyperbola is vertical, the asymptotes will be lines that pass through the center of the hyperbola and have slopes equal to \(\pm\frac{a}{b}\). With the given values of \(a=1.00\) and \(c=-200\) (although \(c\) is not directly used in forming the asymptote equations), you can find \(b\) using the relation \(c^2 = a^2 + b^2\). Once you have \(b\), you plug these values into the equations of the asymptotes: \(y = \pm\frac{a}{b}x\).
However, if the \(c\) value refers to a term in a quadratic equation, it would not be relevant for the hyperbola asymptotes, as they are usually determined by the \(a\) and \(b\) values of the hyperbola equation, with \(b\) being the distance from the center to a vertex along the x-axis for a vertical hyperbola.
The \(c\) value from the quadratic equation might be a part of a different mathematical context and not applicable to finding the hyperbola's asymptotes.