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GATE | GATE 2017 MOCK II | Question 27

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Find the maximum value of the expression (x+y+k) where (x,y) satisfies the equation (x-2)2 + (y-3)2 = 25 (A) (5+k) + 5√2 (B) 5+k (C) 5 + √k (D) 2+k

Answer: (A)

Explanation: Since (X,Y) is a point on circle, the general form of the point is X = 2 + 5*cost, y = 3 + 5*sint We need to maximise the value of x+y+k x+y+k = 2 + 5*cost + 3 + 5*sint + k = (5+k) + 5*(cost+sint) Here, k is a constant. The maximum value of c + acost + bsint is equals to c + sqrt (a*a +b*b). Maximum value of (5+k) + 5*(cost+sint) (5+k) + 5*sqrt(2) The result is (5+k) + 5*sqrt(2).

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Last Updated : 28 Jun, 2021
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