Final answer:
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.