Correct Answer - Option 4 : 9
Concept:
General equation of Parabola is (y - k)2 = 4a(x - h) and its vertex is (h, k).
Calculation:
The equation of parabola is x = y2 - 6y + c
⇒ x = y2 - 6y + 9 - 9 + c
⇒ x = (y - 3)2 - 9 + c
⇒ (y - 3)2 = x + 9 - c
⇒ (y - 3)2 = [x - (c - 9)]
Comparing it with (y - k)2 = 4a(x - h)
Thus vertex is (c - 9, 3)
∵ The vertex lies on y -axis.
⇒ c - 9 = 0 ⇒ c = 9.
Hence, option 4 is correct.