A) \[x+y=1\]
B) \[2(x-y)=5\]
C) \[2x+2y=5\]
D) None of these
Correct Answer: C
Solution :
The other end is \[(t,\,3-t)\] So the equation of the variable circle is \[(x-1)(x-t)+(y-1)(y-3+t)=0\] or \[{{x}^{2}}+{{y}^{2}}-(1+t)x-(4-t)y+3=0\] \ The centre \[(\alpha ,\beta )\] is given by \[\alpha =\frac{1+t}{2},\beta =\frac{4-t}{2}\] Þ \[2\alpha +2\beta =5\] Hence, the locus is \[2x+2y=5\].
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