Question

For what value of k, the points (0, 0), (1, 3), (2, 4) and (k, 3) are con-cyclic.

• A. 2
• B. 1
• C. 4
• D. 5

Answer 1

Answer: (B)

1

Answer 2

The equation of circle through points (0, 0), (1, 3) and

(2, 4) is

$x ^ { 2 } + y ^ { 2 } - 10 x = 0$

Point $( k , 3 )$ will be on the circle, if

$k ^ { 2 } + 9 - 10 k = 0 \Rightarrow k ^ { 2 } - 10 k + 9 = 0$

$k ^ { 2 } - 9 k - k + 9 = 0 \Rightarrow k ( k - 9 ) - 1 ( k - 9 ) = 0$

$\Rightarrow$ $k = 1$ or $k = 9$.