Question

Find the standard form of the equation of the hyperbola satisfying given conditions.see image!

Answer 1

Given

$\begin{gathered} Axis\text{ \lparen-8,0\rparen , \lparen8,0\rparen; Focus \lparen-10,0\rparen,\lparen-10,0\rparen} \\ \\ \end{gathered}$

The standard form of the equation of the hyperbola

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$\begin{gathered} a=8 \\ c=10 \\ b^2=c^2-a^2 \\ b^2=10^2-8^2 \\ b^2=100-64 \\ b^2=36 \\ b=\sqrt{36} \\ b=6 \\ \\ \end{gathered}$

Now substitute into the standard form

$\frac{x^2}{64}-\frac{y^2}{36}=1$

The final answer

Option B