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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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