contestada

Find the vertices and foci of the hyperbola with equation x squared over four minus y squared over sixty = 1.

Respuesta :

again, this one, notice, the positive fraction is the one with the "x" variable in it, thus is also a horizontal hyperbola,

[tex]\bf \cfrac{x^2}{4}-\cfrac{y^2}{60}=1\implies \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{(\sqrt{60})^2}=1\qquad \begin{cases} a=2\\ b=\sqrt{60} \end{cases} \\\\\\ c=\sqrt{2^2+(\sqrt{60})^2}\implies c=\sqrt{4+60}\implies c=8\\\\ -------------------------------\\\\ vertices~~(0\pm 2,0)\implies \begin{cases} (2,0)\\ (-2,0) \end{cases}\qquad foci~~(0\pm 8,0)\implies \begin{cases} (8,0)\\ (-8,0) \end{cases}[/tex]