Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant.

Question

Forneadil · Accepted Answer

We need to fill in the parts of the equation of the sphere (left). In this Formula (h.k,l) is the center and r is the radius.

{(x - h)}^{2} + {(y - k)}^{2} + {(z - l)}^{2} = r^{2}

We were given that the center of our sphere is

(5, 4, 9)

, so we can go ahead and fill in this piece of information. It remains to determine r.

{(x - 5)}^{5} + {(y - 4)}^{2} + {(z - 9)}^{2} = r^{2}

Our sphere must have largest radius that still stays within the first octant. This means we must look at the distance from the center coordinate to each of the three bounding planes: the xy-plane xz-plane, and the yz-plane.

{(x - 5)}^{2} + {(y - 4)}^{2} + {(z - 9)}^{2} = 4^{2}

Find an equation of the largest sphere with center (5,

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