The ends of a quadrant of a circle have the coordinates (1, 3) and (3, 1). Then the center of such a circle is (2, 2) (b) (1, 1) (c) (4, 4) (d) (2, 6)

Options

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

Answer

2

Explanation

If `(alpha,beta)` is the center, then
`(alpha-1)^(2)+(beta-3)^(2)=(alpha-3)^(2)+(beta-1)^(2)` (1)
and `(beta-3)/(alpha-1).(beta-1)/(alpha-3)= -1`
or `(alpha-1)(alpha-3)+(beta-1)(beta-3)=0` (2)
From (1),
`4 alpha -4beta=0`
`:. alpha =beta`
From (2),
`2(alpha-1)(alpha-3)=0`
`:. alpha=1,3`
`:. (alpha,beta)-=(1,1),(3,3)`