Question

STATEMENT -1: The curve $y=\frac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$.

STATEMENT - 2: 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 False, Statement -2 True

Answer 1

The correct option is A Statement -1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement -1

$y=-\frac{x^2}{2}+x+1$

$\Rightarrow 2y=-x^2+2x+2\Rightarrow x^2-2x+1=-2y+3$

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

Clearly this is a parabola with the axis $x-1=0\Rightarrow x=1$

Hence given curve is symmetrical about $x=1$

Hence both statement are correct and Assertion is followed by Reason.