Problem

Show that the equation represents a sphere, and f…

01:17

Problem 18 Easy Difficulty

Show that the equation represents a sphere, and find its center and radius.

$ x^2 + y^2 + z^2 + 8x - 6y + 2z + 17 = 0 $

Answer

center $(-4,3,-1), \quad r=3$

Discussion

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Video Transcript

So in these questions. So the question represent their spears basically this is x squared plus y squared plus b squared. But I guess man a six way six White and plus 2000 plus 17 ecological going to saw that this equals and represent spear and find their centers and radius. I. So we can clearly see that since the the coefficient of a square by square and square one. So we can see and uh there is no extra time, the only X, y and Z. To. So this the presenters pair Okay. And for the radio saying that for the regions and the centre we will find we will make a square. So this is it, that's a square plus old. So this will be like X plus pool is square, Okay, okay, so and there will be a 16 plus over here. So we will just subtract 16 for the balancing out over there plus why minus six y y minus of three square again, nine will be over here plus over nine minus nine. And yet. And plus to get that means jet plus one square one again will be some minus one over here plus 17 equal to the right, so it will be access exploits poor, it's quiet plus y minus of three Squire Plus jet plus of one square. And this is 16 and 9 25. And and it is 26. So this will be a minus of 26 and plus or 17. So it will be like Uh plus -9, that will be nine this side. So we can clearly see that this this will be equal to three is quite so we can clearly see that center have magnitude of the coordinator of this is x minus four minus of four and three and minus 100 G s r equals 23 squares of three. Okay, Thank you.

Manish K.

Topics

Vectors

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Problem