Chapter A5.2, Problem 19E

To determine

To find: the hyperbola’s standard-form equation.

Answer to Problem 19E

The hyperbola’s standard-form equation is $y^2-\frac{x^2}{8}=1$

Explanation of Solution

Given:

Eccentricities $e=3$

Vertices $\left(0,\pm 1\right)$

Calculation:

Given with vertices as $\left(0,\pm 1\right)$ and $e=3$ .

This implies that $a=1$ and $c=3$ .

  $\begin{array}{l}\Rightarrow b=\sqrt{c^2-a^2}\\ \Rightarrow b=\sqrt{8}\end{array}$

The equation hence can be written as,

  $y^2-\frac{x^2}{8}=1$

Conclusion:

Therefore,the hyperbola’s standard-form equation is $y^2-\frac{x^2}{8}=1$