JEE Advanced · Mathematics · 13. Parabola
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.
- A Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
- B Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
- C Statement I is true, Statement II is false
- D Statement I is false, Statement II is true
Answer & Solution
Correct Answer
(A) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
Step-by-step Solution
Detailed explanation
\[
\begin{array}{rlrl}
y & =-\frac{x^2}{2}+x+1 \\
\Rightarrow & y-\frac{3}{2} & =-\frac{1}{2}(x-1)^2
\end{array}
\]
It is symmetric about \(x=1\).
\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 \(x=1\).
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