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Grade: 12


Let x and y be real numbers satisfying the eqn x 2 - 4x + y 2 + 3 =0. If the max and min values of x 2 +y 2 are a and b respectively, then show that the numerical value of a-b is 8

11 years ago

Answers : (1)

Ramesh V
70 Points

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


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)< 4

the numerical value: a-b = 8


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IIT Kgp - 05 batch

11 years ago
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