Let x and y be real numbers satisfying the eqn x² - 4x + y² + 3 =0. If the max and min values of x²+y² are a and b respectively, then show that the numerical value of a-b is 8

the given equation is a circle with centre (2,0) and radius of 1 unit

(x-2)²+x²=1

the genral point on circle in polar form is : ( 2+cos x , sin x )

on putting in x²+y² ,

(2+cos x)²+(sin x)² = -4.sin x

sinx has max. and min. values at 1 , -1

-4 < (2+cos x)²+(sin x)²  < 4

the numerical value: a-b = 8

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