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Question

The centre of the conic section 2x2+4y2+2xy+4x6y+17=0 is

A
(117,87)
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B
(117,87)
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C
(117,87)
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D
(118,78)
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Solution

The correct option is C (117,87)
Let f(x,y)=2x2+4y2+2xy+4x6y+17=0
Partially differentiate w.r.t. x
δfδx=4x+0+2y+40+0=0 (treat y as constant)
2x+y+2=0 (i)

Again, partially differentiate w.r.t. y
δfδy=0+8y+2x6+0=0 (treat x as constant)
x+4y3=0 (ii)
From (i) and (ii),
x=117 and y=87
Then centre is (117,87)

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