False, the given equation of hyperbola is vertical hyperbola.
What is hyperbola?
Hyperbola is defined as a conic section, two-branched open curve, produced by the intersection of a circular cone.
[tex]\frac{(y-2)^2}{16} -\frac{(x+1)^2}{144}=1[/tex]
Simplify each term in the equation in order to set the right side equal to 1
The standard form of an ellipse or hyperbola requires the right side of the equation be 1
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
[tex]\frac{(y-k)^2}{a^2} -\frac{(x-h)^2}{b^2}=1[/tex]
Match the values in this hyperbola to those of the standard form. The variable
h represents the x-offset from the origin,
k represents the y-offset from origin, a.
a=4
b=12
k=2
h=−1
c, the distance from the center to a focus 4√10
The foci is (−1,2+4√10),(−1,2−4√10)
Hence, the hyperbola is vertical.
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