contestada

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 = ?.

The transverse axis of a hyperbola is the xaxis and the equation of the asymptotes is y 43 xIn the equation of the given hyperbola in standard form a b and c class=

Respuesta :

Solution

Asymptomes is

[tex]y=\pm\frac{b}{a}x[/tex]

Compare

[tex]\begin{gathered} y=\pm\frac{4}{3}x \\ \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} c^2=b^2+a^2 \\ c^2=4^2+a^2 \\ c^2=16+9 \\ c=\sqrt{25} \\ c=5 \end{gathered}[/tex]

Therefore

[tex]\begin{gathered} a=3 \\ b=4 \\ c=5 \end{gathered}[/tex]