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Statement I The curve y = x^2/2+x+1 is s...

Statement I The curve `y = x^2/2+x+1` is symmetric with respect to the line `x = 1`. because Statement II A parabola is symmetric about its axis.

A

Statement-1 is True, Statement - 2 is true, Statement-2 is a correct explanation for Statement-1`

B

Statement-1 is True, Statement - 2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is True, Statement - 2 is False.

D

Statement-1 is True, Statement - 2 is True.

Text Solution

Verified by Experts

The correct Answer is:
A
Statement-2 is true, being fundamental property of a parabola.
Now, `y=-x^(2)/2+x+1`
`rArr" "y=-1/2(x^(2)-2x-2)rArry=-1/2{(x-1)^(2)-3}`
`rArr" "y-3/2=-1/2(x-1)^(2)rArr(x-1)^(2)=-2(y-3/2)`
Clearly, it represents a parabola having vertex at (1, 3/2) and axis x=1.
So, it is symmetric with respect to teh line x=1 (by statement-2).
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