Question 603270: Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph
y^2-x^2+2x-6y+7=0
complete the squares
(y^2-6y+9)-(x^2-2x+1)=-7+9-1
(y-3)^2-(x-1)^2=2
(y-3)^2/2-(x-1)^2/2=1
This is a hyperbola with 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.
For given hyperbola:
equation: (y-3)^2/2-(x-1)^2/2=1
Center: (1,3)
a^2=2
a=√2
length of vertical transverse axis=2a=2√2
b^2=2
b=√2
c^2=a^2+b^2=2+2=4
c=√4=2
Foci: (1, 3±c)=(1, 3±2)=(1, 1) and (1,5)
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