Answer to Question #307576 in Analytic Geometry for Cynthia

Question

The equation x2−8 x+y2− 14 y+z2+ 16 z= -113 represents a sphere with radius Blank 1. Calculate the answer by read surrounding text.

and center ( Blank 2. Calculate the answer by read surrounding text.

, Blank 3. Calculate the answer by read surrounding text.

, Blank 4. Calculate the answer by read surrounding text.

).

Answer 1

x² − 8x + y² − 14y + z² + 16z = -113

Let reform this equation in a form:

(x - a)² + (y - b)² + (z - c)² = R², (1)

where R would be radius of the sphere and (a, b, c) - its center.

(x² − 8x + 16) + (y² − 14y + 49) + (z² + 16 z + 64) = -113 + 16 + 49 + 64;

(x - 4)² + (y - 7)² + (z + 8)² = 16;

(x - 4)² + (y - 7)² + (z + 8)² = 4².

From the formula (1) we can say, that this equation represents a sphere with radius R = 4 and center (4, 7, -8).