A sphere S lying in the first octant (where x, y , and z are all ? 0) has its ce

Question

A sphere S lying in the first octant (where x, y, and z are all ? 0) has its center C in the plane with equation z = 5 and is tangent to the xz-plane and to the yz-plane. The

distance from the origin to C is sqrt(43)

(a) Find an equation for S of the form (x ? a)2 + (y ? b)2 + (z ? c)2 = r2.

(b) Find the distance between the origin and the point where S touches the xz-plane.

A sphere S lying in the first octant (where x, y, and z are all ? 0) has its center C in the plane with equation z = 5 and is tangent to the xz-plane and to the yz-plane. The distance from the origin to C is sqrt(43) Find an equation for S of the form (x ? a)2 + (y ? b)2 + (z ? c)2 = r2. Find the distance between the origin and the point where S touches the xz-plane.

Explanation / Answer

Your center is correct however your radius is not. Remember, sqrt(43) is the distance from the Origin to the center, not the sphere to its center.

Since you know that the distance from the center of the sphere to the xz plane is 5and the sphere is tangent to the xzplane, the radius must be 5

(x - 3)^2 + (y - 3)^2 + (z - 5)^2 = 25

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