Finding the equation of a surface?

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In summary, the problem asks for equations of two surfaces. The first surface consists of points where the distance to the x-axis is 5 times the distance to the yz-plane. The second surface consists of points equidistant from the point (-3, 0, 0) and the plane x=3. To solve these problems, we can use the distance formula and manipulate the equations to get the desired forms.
  • #1
Kalookakoo
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Homework Statement



2 Questions.

1)Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is 5 times the distance from P to the yz-plane.

2)Find an equation for the surface consisting of all points that are equidistant from the point (−3, 0, 0) and the plane x = 3.

Homework Equations





The Attempt at a Solution



1)The only thing I can think of is an ellipsoid with an equation similar to 5x^2+y^2+z^2=1

Is that correct? Or am I totally off?

2) I feel a parabolic cylinder would work here (opening facing toward point) but not sure how to find the equation.
 
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  • #2
Kalookakoo said:

Homework Statement



2 Questions.

1)Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is 5 times the distance from P to the yz-plane.

2)Find an equation for the surface consisting of all points that are equidistant from the point (−3, 0, 0) and the plane x = 3.

Homework Equations




The Attempt at a Solution



1)The only thing I can think of is an ellipsoid with an equation similar to 5x^2+y^2+z^2=1

Is that correct? Or am I totally off?

2) I feel a parabolic cylinder would work here (opening facing toward point) but not sure how to find the equation.

In both cases take a variable point ##(x,y,z)##, calculate the various distances, and use the given relations. You will undoubtedly have to square things to simplify the equations.
 

Question 1: What is the process for finding the equation of a surface?

Finding the equation of a surface involves determining the mathematical relationship between the variables that define the surface. This can be done through various methods such as using known points on the surface or using given geometric properties.

Question 2: What are the variables that are used in the equation of a surface?

The variables used in the equation of a surface depend on the type of surface being studied. For example, a 2D surface may have two variables, such as x and y, while a 3D surface may have three variables, such as x, y, and z.

Question 3: Can the equation of a surface be found for any type of surface?

Yes, the equation of a surface can be found for any type of surface, as long as there is enough information available to determine the mathematical relationship between the variables that define the surface.

Question 4: Are there any specific techniques or methods for finding the equation of a surface?

Yes, there are various techniques and methods that can be used for finding the equation of a surface, such as using known points, using geometric properties, or using specific equations for certain types of surfaces (e.g. conic sections).

Question 5: How is the equation of a surface useful in science?

The equation of a surface can be useful in science for understanding and describing the behavior and properties of different types of surfaces, such as in physics for determining the shape of a satellite's orbit or in chemistry for modeling the shape of a molecule.

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