Question

The transverse axis of a hyperbola is the x-axis, and the equation of the asymptotes is y= +- 4/3 x.In the equation of the given hyperbola in standard form a = ?,b = ? and c = ?.

Answer 1

Asymptomes is

`y=\pm(b)/(a)x`

Compare

`\begin{gathered} y=\pm(4)/(3)x \\ \\ \\ \end{gathered}`

`\begin{gathered} c^2=b^2+a^2 \\ c^2=4^2+a^2 \\ c^2=16+9 \\ c=√(25) \\ c=5 \end{gathered}`

Therefore

`\begin{gathered} a=3 \\ b=4 \\ c=5 \end{gathered}`