What would be the best answer for these all 3 problems? always got wrong Safari

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What would be the best answer for these all 3 problems? always got wrong

Safari File Edit View History Bookmarks Window Help G @* 37% D Mon 7:04 PM a OE webassign.net HW 10.1 Chegg Study Guided Solutions and Study Help | Chegg.com Write The Equation Of The Sphere In Standard For l Chegg.com No, they do not lie on a straight line Need Help? Read I Watch It Talk to a Tutor 8. 3/4 points Previous Answers SEssCalc2 10.1.010 My Notes Ask Your Teacher Find an equation of the sphere with center (4, -6, 3) and radius 5. 22+)+2-8x +12y - 6z36 0 Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.) intersection with xy-plane X2 + y -8x + 12y + 36 = 0 | intersection with xz-plane x2 + z2-8-62 + 36 = 0 x intersection with yz-planey Need Help? Read It Talk to a Tutor y+z +12y - 6z +36-0V 9. 1/1 points | Previous Answers SEssCalc2 10.1.011.MI My Notes Ask Your Teacher Find an equation of the sphere that passes through the point (6, 1, -5) and has center (3, 8, 1) 13

Explanation / Answer

xz plane
Lets find whether this works....

x^2 + z^2 - 8x - 6z = -36

Completing squares :
x^2 - 8x + 16 + z^2 - 6z + 9 = -36 + 16 + 9

(x - 4)^2 + (z - 3)^2 = -11

Now, this is impossible innit?
How can addition of two squared terms be a negative 11?

No way, jose!

So, DNE

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10)
x^2 + 4x + y^2 - 6y + z^2 -6z = -6

x^2 + 4x + 4 + y^2 - 6y+ 9 + z^2 - 6z + 9 = -6 + 4 + 9 + 9

(x+2)^2 + (y-3)^2 + (z-3)^2 = 16

So, radius = sqrt16

radius = 4 ----> ANS

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10)
<-6 , 6 , 4>

Lets unitize this ...
|v| = sqrt(36 + 36 + 16)
= sqrt(88)
= 2sqrt22

So, unit vector v = <-6,6,4> / 2sqrt22

Cncel 2 all over :

v = <-3,3,2> / sqrt22

Now, multiply this by 6 :

v = <-18 , 18 , 12> / sqrt(22)

As in
<-18/sqrt22 , 18/sqrt22 , 12/sqrt22> ---> ANS

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