Slope of Asymptote for 6x^2 - {d}y^2 = 6

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Homework Help Overview

The discussion revolves around finding the slope of the asymptote for the hyperbola defined by the equation 6x^2 - {d}y^2 = 6. Participants are exploring the characteristics of hyperbolas and their asymptotes.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the standard form of hyperbolas and how to rewrite the given equation to identify asymptotes. There are inquiries about the behavior of the hyperbola at large values of x and y, and the relevance of the constant in the equation.

Discussion Status

The discussion is ongoing, with participants questioning the relationship between the constant in the equation and the asymptotic behavior of the hyperbola. Some guidance has been offered regarding rewriting the equation, but no consensus has been reached on the specific slope of the asymptote.

Contextual Notes

There is a mention of a variable {d} in the equation, which may introduce ambiguity. Additionally, there are indications of frustration regarding understanding the problem, which could affect the clarity of the discussion.

princiebebe57
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Give the slope of the asymptote for the hyperbola given by the equation 6x^2 - {d}y^2 = 6. Give the value that is positive
 
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What are the asymptotes for the hyperbola
\frac{x^2}{a^2}- \frac{y^2}{b^2}= 1?

Can you put your equation in that form?


Another way to do this: The hyperbola comes close to the asymptote for VERY large values of x and y. Rewrite the equation as 6x^2= dy^2+ 6. Suppose x and y are in the tens of millions. How does the constant "6" compare with the rest of the equation?
 
the constant 6 would always be larger?
 
Is that because 6 is larger than, say, 100000002? You appear to be saying you have no idea how to do these problems. So why are you trying to do them?
 

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