Respuesta :
The third equation hyperbola has one vertex in common with the given hyperbola.
What is a hyperbola?
"A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows".
Given equation,
[tex]\frac{(y - 4)^{2} }{7^{2} }[/tex] - [tex]\frac{(x + 6)^{2} }{8^{2} }[/tex] = 1
If we compare it with the general equation of a hyperbola:
[tex]\frac{(y - k)^{2} }{a^{2} }[/tex] - [tex]\frac{(x - h)^{2} }{b^{2} }[/tex] = 1
Therefore, h = -6, k = 4, a = 7, b = 8
Hence, vertices will be at (h, k ± a).
Therefore, vertices of the given equation of hyperbola is at (-6, 11) and (-6, -3).
Similarly, for the first equation: h = -6, k = 8, a = 5, b = 6.
the vertices of the 1st equation of hyperbola will be at (-6, 13) and (-6, 3).
Similarly, for the second equation: h = 1, k = 11, a = 8, b = 7.
the vertices of the second equation of hyperbola will be at (9, 11) and (-7, 11).
Similarly, for the third equation: h = -15, k = -3, a = 9, b = 5.
the vertices of the third equation of hyperbola will be at (-6, -3) and (-24, -3).
Similarly, for the fourth equation: h = -6, k = 6, a = 6, b = 4.
the vertices of the fourth equation of hyperbola will be at (-6, 12) and (-6, 0).
Similarly, for the fifth equation: h = -6, k = 26, a = 12, b= 8.
the vertices of the fifth equation of hyperbola will be at (-6, 38) and (-6, 14).
Therefore, the third equation hyperbola has one vertex in common with the given hyperbola.
Learn more about hyperbola here: https://brainly.com/question/15793590
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Answer:3rd & 5th equations
Step-by-step explanation:
I don't know what the "expert-verified" answer person did, but this was meant to be a select multiple answers type thing, so I went ahead and did it myself for edmentum.
I found the vertices and the correct equations SHOULD be:
(x + 15)^2 / 9^2 - (y + 3)^2 / 5^2 = 1 (shared vertex is (-6,-3))
and
(y - 23)^2 / 12^2 - (x + 6)^2/8^2 = 1 (shared vertex is (-6,11))
I have yet to check this on Edmentum, but I believe this is right!
