Question

The locus of the centres of the circles for which one end of diameter is $(1,1)$ while the other end is on the line $x+y=3$ is

• A. $x+y=1$
• B. $2(x-y)=5$
• C. $2x+2y=5$
• D. none of these

Answer 1

The correct option is C $2x+2y=5$

Let centre of the circle be $C(h,k)$
And other end of the diameter be $P(a,b)$
Thus $h=\frac{a+1}{2}\Rightarrow a=2h-1$
And $k=\frac{b+1}{2}\Rightarrow b=2k-1$
But point $P(a,b)$ lie on the line $x+y=3$
$\Rightarrow 2h+2k=5$
Hence required locus of $C(h,k)$ is, $2x+2y=5$