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Question

The line segment joining the foci of the hyperbola x2y2+1=0 is one of the diameters of a circle. The equation of the circle is

A
x2+y2=4
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B
x2+y2=2
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C
x2+y2=2
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D
x2+y2=22
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Solution

The correct option is C x2+y2=2
x2y2+1=0
y2x2=1
This is a rectangular hyperbola whose transverse axis is y axis.
c=2
Therefore, coordinates of foci are (0,2),(0,2)
So, equation of the circle with focii as the end points of the diameter is (x0)(x0)+(y2)(y+2)=0
x2+y2=2

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