Question

find an equation of the largest sphere that passes through the point (0, 1, 3) and is such that each of the points (x, y, z) inside the sphere satisfies the condition x²+y²+z² < 136 + 2(x+2y+3z)

Answer 1

To find the equation of the largest sphere that passes through the point (0, 1, 3) and satisfies the condition x²+y²+z² < 136 + 2(x+2y+3z), we can use the form of (x-a)² + (y-b)² + (z-c)² = r². By solving for the center and radius of the sphere, we can find its equation.

Step-by-step explanation:

To find the equation of the largest sphere that passes through the point (0, 1, 3) and satisfies the condition x²+y²+z² < 136 + 2(x+2y+3z), we can start by rewriting the equation in the form of (x-a)² + (y-b)² + (z-c)² = r², where (a, b, c) is the center of the sphere and r is the radius.

To find the equation of the largest sphere that passes through the point (0, 1, 3) and satisfies the condition x²+y²+z² < 136 + 2(x+2y+3z), we can use the form of (x-a)² + (y-b)² + (z-c)² = r². By solving for the center and radius of the sphere, we can find its equation.

From the equation, we can see that the center of the sphere is (2, -4, -2) and the radius can be calculated by substituting the center coordinates into the equation. Finally, the equation of the largest sphere is (x-2)² + (y+4)² + (z+2)² = 72.