Question

Centre and radius of the circle with segment of the line $x+y=1$ cut off by coordinate axes as diameter is:

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

Answer 1

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

Intercepts of $x+y=1$ on coordinate axis :

Put $y=0,$

$\Rightarrow$ $x=1$

and put $x=0,$

$\Rightarrow$ $y=1$

$\therefore$ $(1,0)$ and $(0,1)$

Length = $\sqrt{1^2+1^2}=\sqrt{2}.$

$\therefore$ Diameter $=\sqrt{2}.$

and Centre is mid point of (0,1) & (1,0),

$\because$ Segment between coordinate axis is the diameter.

$\Rightarrow$ $h=\frac{1}{2}andk=\frac{1}{2}.$

$\therefore$ Centre $\to (\frac{1}{2},\frac{1}{2})$

and Radius $=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$