Let x 0 , y 0 be fixed real numbers such that x 0 2 + y 0 2 1 . If x , y are arbitrary real numbers such that x 2 + y 2 ≤ 1 , then the minimum value of x - x 0 2 + y - y 0 2 is

Question

Let x 0 , y 0 be fixed real numbers such that x 0 2 + y 0 2 > 1 . If x , y are arbitrary real numbers such that x 2 + y 2 ≤ 1 , then the minimum value of x - x 0 2 + y - y 0 2 is, x 0 2 + y 0 2 - 1 2, x 0 2 + y 0 2 - 1, x 0 + y 0 - 1 2, x 0 + y 0 2 - 1

MARKS App · Accepted Answer

Let P x 0 , y 0 Given x 2 + y 2 ≤ 1 1$ Let any arbitrary point 8 ( x , y ) . P Q 2 = x - x 0 2 + y - y 0 2 P Q 2 = ( O P - O Q ) 2 P Q 2 = ( O P - O Q ) 2 P Q 2 = x 0 2 + x 0 2 - 1 2 [ ∵ 0 Q = 1 ] ∴ Mininimum value of P Q 2 is x 0 2 + y 0 2 - 1 2

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