Question

The ends of a quadrant of a circle have the coordinates $(1,3)$ and $(3,1)$. The center of such a circle is:

• A. $(2,2)$
• B. $(1,1)$
• C. $(4,4)$
• D. $(2,6)$

Answer 1

The correct option is B $(1,1)$

Let the center be $(x,y)$, then

$3-x=3-y$ ....(since both are radius and equal)

$\Rightarrow x=y$ ...(1)

$(x-3{)}^2+(y-2{)}^2=(x-1{)}^2+(y-3{)}^2$ ...(2)

Using equations (1) and (2), we get $(x,y)=(1,1)$

Hence, option B is correct.