Finding the equation of a surface?

[Kalookakoo]

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.

 

[LCKurtz]

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.