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

• quantizedzeus
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
quantizedzeus
Can anyone tell me how the graph would be if the equation is XY=K(K is constant)?...

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 $(\pm\sqrt{k},\pm\sqrt{k})$

## 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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