Q35 / 66 · JEE Advanced 2007 (Paper 2) · Mathematics
Statement I The curve $y=-\frac{x^2}{2}+x+1$ is symmetric with respect to the line $x=1$
Statement II A parabola is symmetric about its axis.
- Correct answerAStatement I is true, Statement II is true; Statement II is a correct explanation for Statement I
- BStatement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
- CStatement I is true, Statement II is false
- DStatement I is false, Statement II is true
Solution
$$
\begin{array}{rlrl}
y & =-\frac{x^2}{2}+x+1 \\
\Rightarrow & y-\frac{3}{2} & =-\frac{1}{2}(x-1)^2
\end{array}
$$
It is symmetric about $x=1$.
Hence, the correct answer is option: 'A'.