The four distinct points (0, 0),(2, 0), (0, -2) and (k,-2) are co… - Vidyadip

MCQ

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

A
$-2$
✓
$2$
C
$1$
D
$0$

✓

Answer

Correct option: B.

$2$

b
(b) The equation of circle passing through $(0,\,0),\,\,(2,\,0)$ and $(0, -2)$ is

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

If it passes through $(k,\, - 2)$, then ${k^2} + 4 - 2k - 4 = 0$

$ \Rightarrow \,k = 0,\,2$

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

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