Question 412549
Write the standard form of the equation of the conic section with the given charateristics.Hyperbola with vertex at (0, 4), focus at (0, 5), and center at (0, 1)

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Standard form of given hyperbola:
(y-k)^2/a^2-(x-h)^2=1
ctr (0,1)
transverse axis: vertical
a=on the transverse axis, the distance from ctr to vertex=4-1=3
a^2=9
c=on the transverse axis, the distance from ctr to focus=5-1=4
c^2=a^2+b^2
b^2=c^2-a^2=16-9=7

equation of hyperbola:

(y-1)^2/9-(x)^2/7=1

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y=1+((63+9x^2)/7)^.5

{{{ graph( 300, 300, -10, 10, -10, 10, 1+((63+9x^2)/7)^.5,1-((63+9x^2)/7)^.5,1.134x+1,-1.134x+1) }}}