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

(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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