Can anyone tell me how the graph would be if the equation is XY=K(K is

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In summary, the graph of XY=K is a hyperbola with two branches that extend outwards from the origin. The value of K determines the shape and position of the hyperbola, with a larger value resulting in a wider and flatter hyperbola and a smaller value resulting in a narrower and taller hyperbola. There are restrictions on the values of X and Y in this equation, as both cannot equal 0 and any value that makes the denominator equal to 0 would be undefined. The graph can intersect the X or Y axis at the point (K,0) or (0,K), respectively, but not both axes at the same time. To find the coordinates of the vertices and asymptotes, you can
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quantizedzeus
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Can anyone tell me how the graph would be if the equation is XY=K(K is constant)?...
 
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quantizedzeus said:
Can anyone tell me how the graph would be if the equation is XY=K(K is constant)?...

Pretty much like xy=1 except for larger k it would be further out from the origin. It is symmetrical about the line y=x, and intersects this line at [itex](\pm\sqrt{k},\pm\sqrt{k})[/itex]
 

Related to Can anyone tell me how the graph would be if the equation is XY=K(K is

1. What does the graph of XY=K look like?

The graph of XY=K is a hyperbola, with two branches that extend outwards from the origin.

2. How does the value of K affect the graph of XY=K?

The value of K determines the shape and position of the hyperbola. A larger value of K will result in a wider and flatter hyperbola, while a smaller value of K will result in a narrower and taller hyperbola.

3. Are there any restrictions on the values of X and Y in this equation?

Yes, both X and Y cannot equal 0 as this would make the equation undefined. Additionally, any value that makes the denominator (either X or Y) equal to 0 would also be undefined.

4. Can the graph of XY=K intersect the X or Y axis?

Yes, the graph can intersect the X or Y axis at the point (K,0) or (0,K), respectively. However, it will never intersect both axes at the same time.

5. How can I find the coordinates of the vertices and asymptotes of the hyperbola?

The vertices can be found by setting X or Y equal to 0, depending on which axis the vertex lies on. The asymptotes can be found by solving for X or Y in terms of K and setting the resulting equation equal to 0.

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