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

Mathematics

1 answer:

pickupchik [31]2 years ago

6 0

Answer:

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

Step-by-step 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

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