JEE Main 2025 — Parabola Question with Solution
JEE Main 2025 (4 Apr Shift 2)
Question
A line passing through the point , touches the parabola at the point in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-
Choose an option
Show full solutionCorrect option: C
Correct answer
C
Step-by-step explanation
Tangent
$\begin{aligned}
& y=m(x+2) \\ & y^2=x-2 \\ & (m(n+2))^2=n-2 \\ & m^2 x^2+\left(4 m^2-1\right) x+\left(4 m^2+2\right)=0 \\ & D=0 \\ & \left(4 m^2-1\right)^2-4 m^2\left(4 m^2+2\right)=0 \\ & m=\frac{1}{4} \\ & y=\frac{1}{4}(n+2)
\end{aligned}(6,2)\begin{aligned}
& \text { Area } A=\int_0^2\left(\left(y^2+2\right)-(4 y-2)\right) d y \\ & A=\frac{8}{3}
\end{aligned}$
option (3)
$\begin{aligned}
& y=m(x+2) \\ & y^2=x-2 \\ & (m(n+2))^2=n-2 \\ & m^2 x^2+\left(4 m^2-1\right) x+\left(4 m^2+2\right)=0 \\ & D=0 \\ & \left(4 m^2-1\right)^2-4 m^2\left(4 m^2+2\right)=0 \\ & m=\frac{1}{4} \\ & y=\frac{1}{4}(n+2)
\end{aligned}(6,2)\begin{aligned}
& \text { Area } A=\int_0^2\left(\left(y^2+2\right)-(4 y-2)\right) d y \\ & A=\frac{8}{3}
\end{aligned}$
option (3)
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This is a previous-year question from JEE Main 2025, covering the Parabola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.