Question

Assertion :The length of latus rectum of the parabola whose parametric equation is $x=t^2+t+1$ & $y=t^2-t+1$ for $t\in R$ is equal to $2$. Reason: The length of the latus rectum of the parabola $y^2=4ax$ is $4a$.

• 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

Given $t^2+t+1=x$ & $t^2-t+1=y$ On adding & subtracting we get $t=\frac{x-y}{2}$ & $t^2+1=\frac{x+y}{2}$
$\therefore {\left(\frac{x-y}{2}\right)}^2+1=\frac{x+y}{2}$ $\Rightarrow$ $(x-y{)}^2+4=2(x+y)$ $\Rightarrow (x-y{)}^2=2(x+y-2)\Rightarrow Y^2=2X=4aX(a=1/2)\Rightarrow$ Length of latus rectum $=4a=2$
So Assertion and reason both are correct and Assertion followed Reason.