Question

Assertion :The curve $y=\frac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$. Reason: A parabola is symmetric about its axis.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$y=\frac{-x^2}{2}+x+1$ $\Rightarrow 2y=-x^2+2x+2$ or $2y-3=-x^2+2x-1$
$\Rightarrow 2(y-\frac{3}{2})=(x-1{)}^2$
$\Rightarrow X^2=-4\left(\frac{1}{2}\right)Y,X=x-1,Y=y-\frac{3}{2}\Rightarrow$ Curve is symmetric about $X=0$ i.e., $x=1$

$\Rightarrow$ Curve is symmetric about the axis of parabola.

Both Assertion (A) & Reason (R) are true & Reason (R) is the correct explanation of Assertion.