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.

Options

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.

Answer

A

Explanation

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).