Given the following equation of the hyperbola:
[tex]25x^2-16y^2=400[/tex]
The standard form of the hyperbola will be as follows:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
We will rewrite the given equation to be like the standard form:
[tex]\begin{gathered} 25x^2-16y^2=400\rightarrow(\div400) \\ \frac{25x^2}{400}-\frac{16y^2}{400}=\frac{400}{400} \\ \\ \frac{x^2}{16}-\frac{y^2}{25}=1 \\ \\ \frac{x^2}{4^2}-\frac{y^2}{5^2}=1 \end{gathered}[/tex]
Compare the last equation with the standard form:
So, the answer will be as follows:
The value of h = 0
The value of k = 0
The value of a = 4
The value of b = 5
