Question

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

Answer 1

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


`\bf \cfrac{x^2}{4}-\cfrac{y^2}{60}=1\implies \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{(√(60))^2}=1\qquad \begin{cases} a=2\\ b=√(60) \end{cases} \\\\\\ c=\sqrt{2^2+(√(60))^2}\implies c=√(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}`