Step-by-step explanation:
[tex]5 {x}^{2} - 4 {y}^{2} + 80 = 0[/tex]
[tex]5 {x}^{2} - 4 {y}^{2} = - 80[/tex]
[tex] - \frac{ 5{x}^{2} }{16} + \frac{ {y}^{2} }{20} = 1[/tex]
[tex] \frac{ {y}^{2} }{20} - \frac{5 {x}^{2} }{16} = 1[/tex]
To find foci,
[tex]c = \sqrt{ {a}^{2} + b {}^{2} } [/tex]
so
[tex]c = \sqrt{20 + 16} [/tex]
[tex]c = \sqrt{36} [/tex]
[tex]c = ±6[/tex]
Since the y term has a greater denomiator, our foci is
(0,6) and (0,-6)
