SOLUTION: find the vertices and foci of the hyperbola 4x�-y�-48x-4y+40=0

Question 724435: find the vertices and foci of the hyperbola 4x�-y�-48x-4y+40=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the vertices and foci of the hyperbola
4x�-y�-48x-4y+40=0
4x^2-48x-y^2-4y=-40
complete the square:
4(x^2-12x+36)-(y^2+4y+4)=-40+144+4
4(x-6)^2-(y+2)^2=108

This is an equation of a hyperbola with horizontal transverse axis
Its standard form: , (h,k)=(x,y)coordinates of the center.
For given equation:
center: (6,-2)
a^2=27
a=√27≈5.2
b^2=108
c^2=a^2+b^2=27+108=135
c=√135≈11.6
vertices: (6�a,-2)=(6�5.2,-2)=(.8,-2) and (11.2,-2)
foci: (6�c,-2)=(6�11.6,-2)=(-5.6,-2) and (17.6,-2)
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