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Question 454107: Hi, I am studying for a quiz on hyperbolas and one of the problems I am doing is this:
Write an equation in standard form for each hyperbola.
Length of transverse axis 10 and foci at (-7,18) and (-7,-8)
So far, I understand that it is vertical therefore the equation would be in the (y-k)^2/a^2-(x-h)^2/b^2=1
I am pretty sure I also got the center which was (-7, 5)
So now I have (y-5)^2/a^2-(x+7)^2/b^2=1
My problem is is that I don't know how to find what a and b are. I understand they come from the vertices and co-vertices but I don't think I fully understand the transverse axis.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write an equation in standard form for each hyperbola.
Length of transverse axis 10 and foci at (-7,18) and (-7,-8)
So far, I understand that it is vertical therefore the equation would be in the (y-k)^2/a^2-(x-h)^2/b^2=1
I am pretty sure I also got the center which was (-7, 5)
So now I have (y-5)^2/a^2-(x+7)^2/b^2=1
My problem is is that I don't know how to find what a and b are. I understand they come from the vertices and co-vertices but I don't think I fully understand the transverse axis.
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Plot the foci points.
The distance between the foci is 18--8 = 26
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2a + 2c = 26
But length of transverse axis = 2a = 10
So, a = 5
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And 2c = 26-10 = 16
So c = 8
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For a hyperbola a^2+b^2 = c^2
25 + b^2 = 16
b^2 = 9
b = 3
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Since (h,k) = (-7,5)
Equation:
(y-5)^2/25 - (x+7)^2/9 = 1
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Cheers,
Stan H.
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