JEE Main 2021 (Online) 27th August Evening ShiftQuestion 1
The area of the region bounded by the parabola $(y-2)^{2}=(x-1)$, the tangent to it at the point whose ordinate is $3$ and the $x$-axis is :
Application of Integrals
Solution
At $y=3$: $x=2$. $\tfrac{dx}{dy}=2(y-2)=2$, so the tangent is $x-2=2(y-3)$, i.e. $x=2y-4$ (meets x-axis at $(-4,0)$). Parabola $x=1+(y-2)^2$ meets $y=0$ at $x=5$. Area (integrate in $y$ from 0 to 3) $=\int_0^3[1+(y-2)^2-(2y-4)]dy=\int_0^3(y-3)^2dy=9$. Answer: (B).