SOLUTION: I need help "Identifying the vertices and foci of 4x^2-y^2+32x-14y-85=0" Thanks!

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Question 854594: I need help "Identifying the vertices and foci of 4x^2-y^2+32x-14y-85=0" Thanks!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I need help "Identifying the vertices and foci of
4x^2-y^2+32x-14y-85=0
4x^2+32x-y^2-14y=85
complete the square:
4(x^2+8x+16)-(y^2+14y+49)=85+64-49
4(x+4)^2-(y+7)^2=100
(x+4)^2/25-(y+7)^2/100=1
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center
For given hyperbola:
center: (-4,-7)
a^2=25
a=5
vertices=(-4±a,-7)=(-4±5,-7)=(-9,-7) and (1,-7)
b^2=100
b=10
c^2=a^2+b^2=25+100=125
c=√125≈11.2
foci=(-4±c,-7)=(-4±11.2,-7)=(-15.2,-7) and (7.2,-7)