Substitute u=x−7, v=y−3. Then the problem becomes: Find the maximum value of 3u+4v if u2+v2=64. Now substitute: u=k3 and v=l4 then our problem becomes: Find the maximum value of k+l if k2242+l2322=1. But we can substitute k=24sinξ,l=32cosξ hence
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LoginIf x2+y2=14x+6y+6, find the maximum value of 3x+4y
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manpreet![Tuteehub forum best answer]()
Best Answer
3 years ago
Since (x,y)(x,y) is constrained to be in a circle, 3x+4y=733x+4y=73. (The lines 3x+4y=c3x+4y=c and the circle should touch each other and should be as far away as possible from origin. From this, cc can be evaluated). The point of touching gives max value. Another method that can give answer is the Lagrange multiplier but I just learnt it yesterday. Its makes the solution long and its not in my syllabus. Also, I don't know anything about gradients (But I am beginning to love math after reading about it) Is there a simpler solution?