Question 821012
Find an equation for the Hyperbola described.
Focus at (-4,0), Vertices at (-4,4) and (-4,2)
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Given hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
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For given hyperbola:
center:(-4,3)
length of vertical transverse axis=2=2a
a=1
a^2=1
c=3
c^2=9
c^2=a^2+b^2
b^2=c^2-a^2=9-1=8
equation:
{{{(y-3)^2-(x+4)^2/8=1}}}