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

`(x^2)/(a^2)-(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=√(36) \\ b=6 \\ \\ \end{gathered}`

Now substitute into the standard form

`(x^2)/(64)-(y^2)/(36)=1`

The final answer

Option B