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
x2−y2+3=0
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B
2y2−x2+4=0
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C
x2−2y2+4=0
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D
y2−x2+3=0
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Solution
The correct option is Ax2−y2+3=0 Let equation of variable circle is x2+y2+2gx+2fy+c=0, which is centred at (−g,−f)
Given that 2√g2−c=2 and 2√f2−c=4 ⇒g2−c=1 and f2−c=4 ⇒f2−g2=3 ⇒(−f)2−(−g)2=3
Hence, locus of centre is y2−x2=3