SATHEE: Parabola 1 Question 12

Parabola 1 Question 12

12. Statement $I$ 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:

$y = - \frac{x^{2}}{2} + x + 1 \Rightarrow y - \frac{3}{2} = - \frac{1}{2} (x - 1)^{2}$

$\Rightarrow$ It is symmetric about $x = 1$ .

Hence, option (a) is correct.

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Parabola 1 Question 12

12. Statement I The curve y=−x22+x+1 is symmetric with respect to the line x=1. because

Integer Answer Type Questions

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12. Statement $I$ The curve $y = - \frac{x^{2}}{2} + x + 1$ is symmetric with respect to the line $x = 1$ . because