Question

The four distinct points (0, 0),(2, 0), (0, –2) and (k,–2)are con-cyclic, if k =

• A. –2
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (B)

2

Answer 2

The equation of circle passing through $( 0,0 ) , ( 2,0 )$ and (0, – 2) is $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y = 0$. If it passes through $( k , - 2 )$ , then $k ^ { 2 } + 4 - 2 k - 4 = 0$ $\Rightarrow k = 0,2$

$( 0 , - 2 )$ is already a point on circle $\therefore$ k = 2.