The distinct points A 0 ,   0 ,   B 0 ,   1 ,   C 1 ,   0 and D 2 a ,   3 a are concyclic, then

Step-by-step solution

Since, B and C are the ends of diameter as ∠ B A C is 90 ° We know that equation of circle having endpoints of diameter as x 1 , y 1 and x 2 , y 2 is given as x - x 1 x - x 2 + y - y 1 y - y 2 = 0 Here, the endpoints of diameter are 0 , 1 and 1 , 0 ∴ Equation of circle is x x - 1 + y y - 1 = 0 ⇒ x 2 + y 2 - x - y = 0 Now, point D satisfies this equation ⇒ 4 a 2 + 9 a 2 - 5 a = 0 ⇒ a 13 a - 5 = 0 ⇒ a = 0 ,   a = 5 13