Find an equation for the hyperbola.

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Homework Help Overview

The discussion revolves around finding the equation of a hyperbola given specific conditions, including the foci and the length of the transverse axis. Participants are exploring the relationships between the parameters of the hyperbola, specifically focusing on the values of \(a\), \(b\), and \(c\).

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the foci and the transverse axis length, attempting to derive values for \(a\) and \(b\). There is confusion regarding the calculations and the application of the Pythagorean relation \(c^2 = a^2 + b^2\). Some participants question the interpretation of the transverse axis length and how it relates to the values of \(a\) and \(b\).

Discussion Status

The conversation is active, with participants sharing their calculations and reasoning. Some guidance has been offered regarding the use of the Pythagorean relation to find \(b\), and there is a recognition of errors in earlier calculations. Participants are collaboratively working through the problem, but no consensus has been reached on the final equation.

Contextual Notes

There is an ongoing discussion about the correct interpretation of the transverse axis length and its implications for the values of \(a\) and \(b\). Participants are also addressing potential misunderstandings in their calculations.

wat2000
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Find an equation for the hyperbola that satisfies the given conditions. Foci (0, ±7), length of transverse axis 7. I am a little confused on how to solve this. I tried to solve it and I've found that c^2= 49 so I know that a^2 and b^2 must add up to 49 but I am not sure what my next step is. Can someone help me?
 
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wat2000 said:
Find an equation for the hyperbola that satisfies the given conditions. Foci (0, ±7), length of transverse axis 7. I am a little confused on how to solve this. I tried to solve it and I've found that c^2= 49 so I know that a^2 and b^2 must add up to 49 but I am not sure what my next step is. Can someone help me?

If by "the length of the transverse axis" you mean the distance between the intercepts, then you would have 2a = 7. That should help.
 
so a would equal 2/7? Do i solve 2a=7 to create that fraction?
 
Last edited:
wat2000 said:
so a would equal 2/7? Do i solve 2a=7 to create that fraction?

You mean 7/2. :cry: Now find b.
 
yes I mean 7/2. anyway i don't know how to find b. the only thing i can think of is to square 7/2 and 7 to give me 7/4 and 49 and then subtract them to give me b. that doesn't work though. what's my next step?
 
js14 said:
yes I mean 7/2. anyway i don't know how to find b. the only thing i can think of is to square 7/2 and 7 to give me 7/4 and 49 and then subtract them to give me b. that doesn't work though. what's my next step?
Yes, you need to use the Pythagorean relation
c^2 = a^2 + b^2
to find b. What do you mean, it "doesn't work"? Show us what you got.
 
ok I have it now. i was looking at it wrong. 7/2 squares to 49/4 so a^2=49/4. and when i use the formula c^2 = a^2 + b^2 to find b^2. i plug 7 into c^2 and 49/4 into a^2. this gives me (7)^2=49/4 +b^2. then i square 7 to give me 49=49/4+b^2 then subtract 49/4 to get b^2 by itself and I get 147/4 = b^2. and since the foci points are (0, ±7) the y^2 should be out front.
y^2/(49/4) + x^2/(147/4) =1. and this simplifies to 4y^2/49 + 4x^2/147 = 1. and that's the final answer.
 

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