JEE 2024 — Mathematics PYQ

Given four points lie on circle.
So, the equation of circle is
$(x-1)(x-0)+(y-0)(y-1)=0$
$⟹x^2-x+y^2-y=0\dots \text{(i)}$
$\because (2k,3k)$ lie on (i), we get
$⟹(2k{)}^2-2k+(3k{)}^2-3k=0$
$⟹13k^2-5k=0⟹k(13k-5)=0$
$⟹k=0\text{ or }k=\frac{5}{13}$
$\therefore \text{Value of }k=\frac{5}{13}$