Luisito7592 Luisito7592
  • 26-04-2022
  • Mathematics
contestada

Which are the foci of the hyperbola represented by 5x2 – 4y2 + 80 = 0?

Respuesta :

algebraic12 algebraic12
  • 26-04-2022

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)

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