Question

If the line x + y –1 = 0 touches the parabola y² = kx, then the value of k is

• A. 4
• B. –4
• C. 2
• D. –2

Answer 1

Answer: (B)

–4

Answer 2

Any tangent to y² = kx is y = mx +k/m. Comparing it with given line y = 1-x, we get, m = -1 and k/4m1

⇒ k = -4.

Alternative:

If x+ y –1 = 0 touches y² = kx, then y² = k(1-y) would have equal roots ⇒ k² + 4k = 0 ⇒ k = 0 or -4. But k ≠ 0 , hence k = -4