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The maximum possible value of x^(2)+y^(2...

The maximum possible value of `x^(2)+y^(2)-4x-6y, x, y in RR` subject to the condition `|x+y|+|x-y|=4`

A

is 12

B

is 28

C

is 72

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B

`|x+y|+|x-y|=4` represent a square
`x^(2)+y^(2)-4x-6y=(x-2)^(2)+(y-3)^(2)-13`
`=("distance point on square from "(2, 3))^(2)-13`
Maximum `=(-2-2)^(2)+(-2-3)^(2)-13=28`
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