# Points on the curve of intersection

• crazykizzat
In summary, the conversation is about finding the points on the curve of intersection between x^2+(y-1)^2+(z-1)^2=1 and 2x+y+2z=4, as well as determining the nearest and furthest points from the origin and the minimum and maximum distances. The person is unsure of how to approach the problem and mentions the possibility of solving for a variable and using Lagrange multipliers.
crazykizzat
hi i need to find the points on the curve of intersection of x^2+(y-1)^2+(z-1)^2 = 1 and 2x + y + 2z = 4 which are nearest and furthest furthest from the origin. Also the min and max distances. I'm not looking for you guys to do this four me, I'm kind of lost and don't know where to go. I think I'm supposed to solve one of teh equations for a variable such as y = 4 - 2x - 2z and plug it into the other equation to get the curve of intersection but i;m not sure what to do from there and if that's even correct. I think my teacher also said something about setting one of the equations = to z cause tahts going to be the maximum.

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This sounds like a Lagrange multipliers problem!

## 1. What is the significance of points on the curve of intersection?

Points on the curve of intersection are important because they represent the points where two curves, surfaces, or objects intersect. These points can provide valuable information about the relationship between the two objects or the behavior of the curves.

## 2. How can points on the curve of intersection be calculated?

The calculation of points on the curve of intersection depends on the type of curves or surfaces involved. In some cases, the equations of the curves can be solved simultaneously to find the coordinates of the points. In other cases, numerical methods or computer algorithms may be used to approximate the points.

## 3. Can points on the curve of intersection be used in real-world applications?

Yes, points on the curve of intersection have many practical applications. For example, in engineering and architecture, these points can be used to determine the intersection of two beams or the meeting point of two walls. In physics and mathematics, these points can be used to analyze the behavior of intersecting curves or surfaces.

## 4. How do points on the curve of intersection relate to the concept of derivatives?

Points on the curve of intersection can be used to find the derivative of a function at a specific point. This is because the tangent lines of the two intersecting curves at the point of intersection will have the same slope, which is equal to the derivative of the function at that point.

## 5. Are points on the curve of intersection always visible or easily identifiable?

No, points on the curve of intersection may not always be visible or easily identifiable. In some cases, the curves or surfaces may overlap or intersect at multiple points, making it difficult to pinpoint a specific point of intersection. Additionally, in 3D space, the points may not be visible unless viewed from a specific angle.

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