IIT JEE Advanced 2007 Paper 2

We have
y = −

x2

2

+x+1
2y = −x2+2x+2
- 2y = x2−2x−2
- 2y + 2 = x2−2x
- 2y + 2 + 1 = x2−2x+1
⇒ - 2y + 3 = (x−1)2
⇒ (x−1)2 = - 2 (y−

3

2

)
Since x = 1 is the axis of parabola, the curve is symmetric about the line x = 1.
Therefore, both statements are true and Statement-2 is the correct explanation of Statement-1.