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Let x and y be real numbers satisfyingthe equation x 2 -4x+y 2 +3=0. If the maximum and minimum values of x 2 + y 2 are M and m respectively, then the numerical value of M-m is ? A) 2 B) 8 C) 15 Give an explanation for your answer.

 Let x and y be real numbers satisfyingthe equation x2-4x+y2+3=0. If the maximum and minimum values of x2+ y2 are M and m respectively, then the numerical value of M-m is ?


A) 2      B) 8       C) 15


Give an explanation for your answer.


 

Grade:upto college level

1 Answers

Yuvraj
21 Points
7 years ago
x^2+y^2-4x+3=0 So (x-2)^2+y^2=1 which is circle with center (2,0) and radius 1 Therefore parametrically, x=2+cos t y=sin t where t is the parametric angle so x^2+y^2=5+4cos t Differentiating, we get -4sin t which should be zero for max and min values so t=0 or p So M=5+4cos(0)=9 m=5+4cos(p)=1 So M-m=8

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