Respuesta :

absor201

Answer:

  • (x₁, y₁) = (2, 1)
  • a = 4, b = 2

Step-by-step explanation:

The standard form equation of a hyperbola is

[tex]\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1[/tex]

Here:

  • center (x₁, y₁) = (h, k)
  • 'a' is semi-axis and 'b' is semi-conjugate axis 'b'

Given the equation

[tex]\frac{\left(x-2\right)^2}{4^2}-\frac{\left(y-1\right)^2}{2^2}=1[/tex]

comparing with the  standard form equation of a hyperbola

(x₁, y₁) = (h, k) = (2, 1)

a = 4, b = 2

Therefore,

  • (x₁, y₁) = (2, 1)
  • a = 4, b = 2

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