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Question 471422: write the equation of hyperbola c entered in (2,1) with foci (2,-3) and (2,5) and asymptote y=x-1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write the equation of hyperbola centered in (2,1) with foci (2,-3) and (2,5) and asymptote y=x-1
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This is a hyperbola with vertical transverse axis.Could tell from coordinates of Foci.
Standard form of hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1
From equation of asymptote, y=x-1, its slope, m=1, and y-intercept=-1
a/b=m=1
a=b
c=4 (Could also tell from coordinates of Foci.)
c^2=a^2+b^2=a^2+a^2=2a^2
16=2a^2
a^2=16/2=8
a=√8
a^2=8
b^2=8
Equation:
(y-1)^2/8-(x-2)^2/8=1
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Asymptotes:
y=x-1 (given)
Other asymptote: y=-mx+b
Use (x,y) coordinates of center to find b
1=-1(2)+b
b=3
equation of 2nd asymptote: y=-x+3
see graph below as a visual check on the answer
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y=±(8+(x-2)^2)^.5+1
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