Question

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

• A. 0
• B. 1
• C. $\frac{5}{13}$
• D. $\frac{13}{7}$

Answer 1

Answer: (C)

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