WBJEE 2016 Math Solved Paper

Solving x2 = ay with y - 2x = 1,
x2 = a (1 + 2x) ⇒ x2 - 2ax - a = 0
Let x1 & x2 are the roots
So, (x1−x2)2 = (2a)2 - 4 (-a) = 4a (a + 1)
also, (y1−y2)2 = ((2x1 + 1) - (2x2+1))2 = 4(x1−x2)2 = 16a (a + 1)
now v(x1−x2)2+(y1−y2)2 = √4a(a+1)+16a(a+1) = √40
⇒ 20a (a + 1) = 40 ⇒ a2 + a - 2 = 0 ⇒ a = -2, 1