Question
Let the image of parabola x^ 2 =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
JEE Main
Mathematics
Parabola
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 8
- B. 6
- C. 12
- D. 4
Answer
B. 6
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.
Related: Mathematics — Parabola · All PYQ Banks