Question

The centre and the radius of the circle with the segment of the line $x+y=1$ cut off by the coordinate axes as a diameter

• A. $(1,1),\sqrt{2}$
• B. $(\frac{1}{2}\frac{1}{2})$ , $\sqrt{2}$
• C. $(\frac{1}{2},\frac{1}{2})$ , $\frac{1}{\sqrt{2}}$
• D. $(0,0),1$

Answer 1

The correct option is C $(\frac{1}{2},\frac{1}{2})$ , $\frac{1}{\sqrt{2}}$

AB is a diameter of required circle
So, centre is mid-point of AB
$C\equiv (1/2,1/2)$
and radius $=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$