Parabola 1 Question 12
12. Statement $\mathbf{I}$ The curve $y=-\frac{x^{2}}{2}+x+1$ is symmetric with respect to the line $x=1$. because
(2007, 3M)
Statement II A parabola is symmetric aboutits axis.
(a) Statement I is correct, Statement II is correct, Statement II is a correct explanation for Statement I
(b) Statement I is correct, Statement II is correct, Statement II is not a correct explanation for Statement I
(c) Statement I is correct, Statement II is incorrect
(d) Statement I is incorrect, Statement II is correct
Integer Answer Type Questions
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Answer:
Correct Answer: 12. (4)
Solution:
- $y=-\frac{x^{2}}{2}+x+1 \Rightarrow y-\frac{3}{2}=-\frac{1}{2}(x-1)^{2}$
$\Rightarrow \quad$ It is symmetric about $x=1$.
Hence, option (a) is correct.
