Let the image of parabola x²=4 y , in the line x-y=1 be (y+a)²=b(x-c) , a, b, c ~N . Then a+b+c is equal to

Step-by-step solution

Reflection of point (h, k) in line x - y - 1 = 0 : x-h 1 = y-k -1 = -2(h-k-1) 2 = k - h + 1 . Image: (k+1, h-1) . Let (X, Y) = (k+1, h-1) , so h = Y+1, k = X-1 . From h^2 = 4k : (Y+1)^2 = 4(X-1) . Comparing with (y+a)^2 = b(x-c) : a = 1, b = 4, c = 1 . a + b + c = 1 + 4 + 1 = 6 .