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Question

The equation (x2)2+y2(x+2)2+y2=5 represents

A
a hyperbola
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B
an ellipse
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C
line segment
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D
an empty set
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Solution

The correct option is D an empty set
Let point A be (2,0) and B be (2,0).
Let P be (x,y).
LHS of the given equation is PAPB.
AB=4
By triangle inequality,
PAPB<AB
But in the given equation, PAPB=5 .
AB=4.
This is not possible. Hence, the equation represents an empty set.

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