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Parabola question

2025 · Shift 2 · Q22

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PYQ Library
JEE Advanced
Mathematics
Parabola
2025 · Shift 2 · Q22

Parabola question

2025 · Shift 2 · Q22

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2

Let

S

denote the locus of the mid-points of those chords of the parabola

y^2=x

, such that the area of the region enclosed between the parabola and the chord is

\frac{4}{3}

. Let

\mathcal{R}

denote the region lying in the first quadrant, enclosed by the parabola

y^2=x

, the curve

S

, and the lines

x=1

and

x=4

. Then which of the following statements is (are) TRUE?

A
$(4, \sqrt{3}) \in S$
B
$(5, \sqrt{2}) \in S$
C
Area of $\mathcal{R}$ is $\frac{14}{3} - 2\sqrt{3}$
D
Area of $\mathcal{R}$ is $\frac{14}{3} - \sqrt{3}$

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