Find an equation of the largest sphere with center (5, 3, 6) and is contained in the first octant. Be sure your formula is monic.

Question

I had put the equation as:

 

(x-5)^2+(y-3)^2+(z+6)^2

 

However it was viewed as incorrect. Also they had that it equaled zero.

 

equation input = zero.

Answer 1

Hello Anablele,

For the sphere to stay in the first octant, the radius can't be bigger than 3, otherwise it would cross the xz-plane.

 

So to complete the equation of the sphere, set the expression you have equal to 3², e.i.

(x-5)²+(y-3)²+(z+6)² = 3².

 

Since they want it monic, expand everything and move the 3² over to get it equal to zero,

→ x² - 10x +25 + y² - 6y + 9 + z² + 12z + 36 - 9 = 0

→ x² - 10x + (y² - 6y + z² + 12z + 61) = 0

 

I hope the above helps, and thank you for posting the question.

 

Michael E.