SOLUTION: Find the vertices, foci, and center of the hyperbola. Graph the equation. 4y^2 - x^2 - 2x

SOLUTION: Find the vertices, foci, and center of the hyperbola. Graph the equation. 4y^2 - x^2 - 2x - 16y + 11 = 0

Question 854643: Find the vertices, foci, and center of the hyperbola. Graph the equation.
4y^2 - x^2 - 2x - 16y + 11 = 0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the vertices, foci, and center of the hyperbola. Graph the equation.
4y^2 - x^2 - 2x - 16y + 11 = 0
4y^2-16y -x^2-2x=-11
complete the square:
4(y^2-4y+4) -(x^2+2x+1)=-11+16-1
4(y-2)^2-(x+1)^2=4

This is an equation of a hyperbola with vertical transverse axis.
Its standard form of equation: , (h,k)=coordinates of center
For given hyperbola:
center: (-1,2)
a^2=1
a=1
vertices: (-1,2�a)=(-1,2�1)=(-1,1) and (-1,3)
b^2=4
b=2
c^2=a^2+b^2=1+4=5
c=√5≈2.2
foci: (-1,2�c)=(-1,2�2.2)=(-1,-.2) and (-1,4.2)
see graph below:
y=(1+(x+1)^2/4)^.5+2

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