Question 502428: Determine the coordinates of the foci of the hyperbola : y2-2x2-4x-4y=0.
(Round off answer to nearest hundredths.)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Determine the coordinates of the foci of the hyperbola : y2-2x2-4x-4y=0.
(Round off answer to nearest hundredths.)
**
y2-2x2-4x-4y=0
complete the squares
(y^2-4y+4)-2(x^2+2x+1)=4-2=2
(y-2)^2-2(x+1)^2=2
(y-2)^2/2-(x+1)^2/1=1
This is a hyperbola with vertical transverse axis of the standard form:
(y-k)^2/a^2-(x-h)^2,b^2=1
For given equation:
Center: (-1, 2)
a^2=2
b^2=1
c^2=a^2+b^2=2+1=3
c=√3
..
Foci: (-1, 2±c)=(-1, 2±√3)=(-1, 2+√3) and (-1, 2-√3)=(-1, 3.73) and (-1, .27)
ans:
Coordinates of the Foci: (-1, 3.73) and (-1, 0.27)
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