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Question

If the intercepts of the variable circle on the x and y-axis are 2 units and 4 units respectively, then the locus of the centre of the variable circle is

A
x2y2+3=0
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B
2y2x2+4=0
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C
x22y2+4=0
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D
y2x2+3=0
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Solution

The correct option is A x2y2+3=0
Let equation of variable circle is x2+y2+2gx+2fy+c=0, which is centred at (g,f)

Given that 2g2c=2 and 2f2c=4
g2c=1 and f2c=4
f2g2=3
(f)2(g)2=3
Hence, locus of centre is y2x2=3

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