Question

Let x and y be real numbers satisfying the equation x² – 4x + y² + 3 = 0. If the maximum and minimum values of x² + y² are a and b respectively. Then the numerical value of a – b is ______.

Options

• 1

• 2

• 7

• 8

Answer 1

Let x and y be real numbers satisfying the equation x² – 4x + y² + 3 = 0. If the maximum and minimum values of x² + y² are a and b respectively. Then the numerical value of a – b is 8.

Explanation:

(x – 2)² + y² = 1

ℓ_max = (3)² = 9 = a

ℓ_min = (1)² = 1 = b

a – b = 8