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Expert: Josh - 12/13/2005


Question
what is this equation called x*y=constant ?

Answer
Hi Jai,

This equation depicts a hyperbola.
Let "k" be an arbitrary "non-zero" constant.
Rearranging this, you'll see that x=k/y.
It shows that x varies in inverse proportion with y.

A simple example should assure you of this.
Suppose that k=1. Then, we have x=1/y OR y=1/x.
Restricting our attention to positive values of x,
(i) As x goes toward 0, y tends toward some large value (positive infinity).
(ii) As x tends toward a large positive value, y approaches 0.
So, the x-axis, and y-axis give you the asymptotes, i.e., limiting values which the curve approaches as values get big.

Similar consideration will reveal that a branch is also defined in the "third" quadrant, for negative values of both x and y.

Cheers.

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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