Using the equation of the hyperbola, it is found that the statement is false.
Equation of an hyperbola:
The equation of an hyperbola of center [tex](x_0,y_0)[/tex] is given by:
[tex]\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1[/tex]
The foci are given by: [tex](x_0 - c, y_0)[/tex] and [tex](x_0 + c, y_0)[/tex].
In which [tex]c^2 = a^2 + b^2[/tex]
In this problem, we have that the parameters are given by:
[tex]x_0 = 2, y_0 = -1, a^2 = 36, b^2 = 64[/tex].
Then:
[tex]c^2 = a^2 + b^2[/tex]
[tex]c^2 = 100[/tex]
[tex]c = 10[/tex]
The foci are given by:
[tex](x_0 - c, y_0) = (2 - 10, -1) = (-8, -1)[/tex]
[tex](x_0 + c, y_0) = (2 + 10, -1) = (12, -1)[/tex]
Hence, the statement is false.
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