Question

identify the quadric surface of x^2+y^2+z^2+127=0

Answer 1

the left hand side is always positive, the right hand side is zero

they can't be equal for any real numbers x,y and z.

Answer 2

so you mean that this has no quadric surface?

Answer 3

yes. no triple (x,y,z) will satisfy the equation.

Answer 4

ah so whats the best reason that i can say to my profeesor if ever i was ask in by her?

Answer 5

it's a 3D counterpart of a degenerate curve.

in analytic geometry, it is possible that an equation, say of a circle \[x^2 + y^2 + Dx + ey + F =0\]
to have no solution, from which we say the circle is degenerate.

this idea extends to surfaces and curves in 3D, too.

Answer 6

here's a clear comparison

\[x^2+y^2+z^2=64\] sphere; \(C(0,0,0), r=8\)

\[x^2+y^2+z^2=0\] point sphere at \(C(0,0,0)\)

\[x^2+y^2+z^2=-127\] degenerate sphere

Answer 7

@Wencester do you see why? Whenever you square a real number, the result is always positive... there's no way to square three numbers and add them for a neg. result.

Answer 8

thnks for that but what if the equation will be \[x ^{2}+y ^{2}+z ^{2}=127\]

Answer 9

Then you have a sphere, of radius sqrt(127).

Answer 10

@agent0smith i agree

Answer 11

\[x^2+y^2+z^2=r^2 \]^ equation of a sphere at the origin.

Answer 12

@Wencester have you read the central and non-central quadric surfaces?

Answer 13

not yet sir... whats up on that?

Answer 14

you should read them, in addition to asking questions.

Answer 15

ah ok tnx ill read on it

Answer 16

type it here, @Wencester

Answer 17

how will i know the rate of chnge in atmospheric pressure using a contour plt...if the distance between the two location is 1400 miles

Answer 18

it based on the contour pot wherein the level of curves are given

Answer 19

do you have an equation?

Answer 20

nothing

Answer 21

how about the plot?

Answer 22

its in my photocopy..its hard to draw