Question

Traces of surface x2 + y2 − z2 = 1. Determine the equation for the family of traces in x = n.

Answer 1

`\mathbf{y^2 -z^2 =1- n^2}`

Explanation:

Give that:

the surface equation is
`x^2 +y^2 -z^2 =1`

from the family of traces in x = n given that
`x^2 +y^2 -z^2 =1` , the equation can be represented as :

`n^2 +y^2 -z^2 =1`

`\mathbf{y^2 -z^2 =1- n^2}`

This represents a family of hyperbola for all values of n expects that n = ± 1

So, if n = ± 1,

Then

`y^2 - z^2 = 0`

(y-z) (y+z) = 0

y = ± z

So, for n = ± 1, it is a pair of line for y = z, y = -z