Problems from Reduced equation of the horizontal hyperbola

Development:

$e=4$ is chosen. With $e={\displaystyle \frac{c}{a}}\Rightarrow a={\displaystyle \frac{c}{e}}={\displaystyle \frac{4}{4}}=1$.

As $c^2=a^2+b^2\Rightarrow b=\sqrt{c^2-a^2}=\sqrt{16-1}=\sqrt{15}$.

Substituting in ${\displaystyle \frac{x^2}{a^2}}-{\displaystyle \frac{y^2}{b^2}}=1$ the equation is obtained $${\displaystyle \frac{x^2}{1}}-{\displaystyle \frac{y^2}{15}}=1$$

Solution:

For $e=4$, the equation is ${\displaystyle \frac{x^2}{1}}-{\displaystyle \frac{y^2}{15}}=1$.

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