SOLUTION: Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 81 minus the quantity of y minus 3 squared divided by 144 = 1. choices below Vert

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Question 1138243: Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 81 minus the quantity of y minus 3 squared divided by 144 = 1.
choices below
Vertices: (4, 3), (-14, 3); Foci: (-20, 3), (10, 3)

Vertices: (3, 7), (3, -17); Foci: (3, -17), (3, 7)

Vertices: (7, 3), (-17, 3); Foci: (-17, 3), (7, 3)

Vertices: (3, 4), (3, -14); Foci: (3, -20), (3, 10)
Answer by MathLover1(20850) About Me  (Show Source):
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Find the vertices and foci of the hyperbola with equation quantity
%28x+%2B5%29%5E2%2F+81+-+%28+y-3%29%5E2+%2F144+=+1+
compare to standard form:
%28x+-h%29%5E2%2F+a%5E2+-+%28+y-k%29%5E2+%2Fb%5E2=+1+
it's Right-left Hyperbola with:
=> a%5E2=81=>a=9
=> b%5E2=144=>b=12
=> h=-5,k=3
the center is at (h, k)
=> center is at:(-5,3)

c%5E2=a%5E2%2Bb%5E2
c%5E2=144%2B81
c=sqrt%28225%29
c=15
the foci are at (h%2Bc,+k ), (h-c,+k )

=>the foci are at (-20,+3) , (10,+3)
the vertices are at (h%2Ba,+k ), (h-a, k )
=>the vertices are at (4,+3) and (-14, 3)

answer:
Vertices: (4,+3), (-14, 3); Foci:(-20,+3) , (10,+3)