Answer:
The vertices of the hyperbola are (17,6) and (-1,6).
Step-by-step explanation:
What is hyperbola?
A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone.
What is vertices?
Vertices in shapes are the points where two or more line segments or edges meet (like a corner).
Given the equation of the hyperbola,
[tex]\frac{(y+6)^{2} }{81} -\frac{(x+8)^{2} }{49} =1[/tex]
The general formula for the hyperbola is,
[tex]\frac{(y+k)^{2} }{a^{2} } -\frac{(x+h)^{2} }{b^{2} } =1[/tex]
Here the values are,
a= 9 , b = 7 , h = 8, k = 6
The vertices are (h+a,k), (h-a,k) = (8+9, 6), (8-9, 6) = (17,6), (-1, 6).
To know more about vertices, hyperbola here
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