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If the vertex of the parabola x = y2 - 6y + c lies on y -axis, then the value of c is ?
1. 3
2. -3
3. -9
4. 9

1 Answer

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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.

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