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  4. Value of k for which four distinct points (2 k, 3 k),(1,0),(0,1),(0,0) lies on a circle is

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Q. Value of $k$ for which four distinct points $(2 k, 3 k),(1,0),(0,1),(0,0)$ lies on a circle is

Conic Sections

Solution:

Circle passing through $(1,0),(0,0) \&(0,1)$
$x^2+y^2-x-y=0$
$(2 k, 3 k)$ lies on it if $4 k^2+9 k^2-2 k-3 k=0$
$\Rightarrow 13 k^2-5 k=0 $
$ \Rightarrow k=0 $ or $ \frac{5}{13}$