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Question

If the equation (x1)2+(y2)2=λ|x+y+3| represents a parabola, then

A
λ=1
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B
λ=13
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C
Coordinates of focus are (1,2)
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D
Coordinates of focus are (1,0)
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Solution

The correct option is C Coordinates of focus are (1,2)
The given equation is (x1)2+(y2)2=λ|x+y+3|
Squaring both sides, we get
(x1)2+(y2)2=λ(x+y+3)2
(x1)2+(y2)2=2λ(x+y+32)2
Above equation represents parabola if
2λ=1
λ=12
The focus of the parabola is (1,2)

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