GATE | GATE 2017 MOCK II | Question 27
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
(C) 5 + √k
Explanation: Since (X,Y) is a point on circle, the general form of the point is
X = 2 + 5*cost, y = 3 + 5*sint
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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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