Find the equation of the sphere

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SUMMARY

The equation of the sphere centered at (-6, -7, -1) with a radius of 9 is given by (x + 6)² + (y + 7)² + (z + 1)² - 9² = 0. To find the intersection of this sphere with the plane z = 0, the equation simplifies to (x + 6)² + (y + 7)² - 80 = 0. This transformation effectively replaces z with 0 in the original sphere equation, allowing for the calculation of the intersection in a two-dimensional plane.

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Find the equation of the sphere centered at (-6,-7,-1) with radius 9.

well i got (x+6)^2 + (y+7)^2 + (z+1)^2-9^2 which is correct.

now for the next question:

Give an equation which describes the intersection of this sphere with the plane z=0.

i don't understand how to do the second question at all, can someone help?
 
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What you got must've been:
(x+6)^2 + (y+7)^2 + (z+1)^2-9^2 = 0.

The equation that describes the intersection with the plane z = 0 must be:
(x+6)^2 + (y+7)^2 + (0+1)^2-9^2 = (x+6)^2 + (y+7)^2 - 80 = 0
 
thanks a lot, i get it now
 

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