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Question

The centre of the conic represented by the equation x26xy+y2+6x+14y2=0 is

A
(3,2)
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B
(3,4)
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C
(3,4)
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D
(5,4)
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Solution

The correct option is A (3,2)
Let f(x,y)=x26xy+y2+6x+14y2=0
Partially differentiate w.r.t. x and equate to zero
δfδx=2x6y1+0+6+0+0=0 (treat y as constant)
x3y+3=0 (1)

Again, partially differentiate w.r.t. y and equate to zero
δfδy=6x+2y+14=0 (treat x as constant)
y3x+7=0 (2)
Solving (1) and (2),
x=3 and y=2
Centre of given conic is (3,2)

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