Hyperbola JEE Main PYQs PDF, 2020–2026

Hyperbola questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 62 of the 63 asked.

Topic-wise weightage by year

How many Hyperbola questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

All 12 JEE Main 2026 Hyperbola questions in the free PDF, latest shift first.

1. JEE Main 2026 · 6 Apr · Shift 1 · Standard Equation

   If the eccentricity $e$ of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, passing through $(6,4\sqrt{3})$, satisfies $15\left(e^{2}+1\right)=34e$, then the length of the latus rectum of the hyperbola $\frac{x^{2}}{b^{2}}-\frac{y^{2}}{2(a^{2}+1)}=1$ is:

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2. JEE Main 2026 · 6 Apr · Shift 2 · Standard Equation

   The eccentricity of an ellipse $E$ with centre at the origin $O$ is $\frac{\sqrt{3}}{2}$ and its directrices are $x=\pm \frac{4\sqrt{6}}{3}$. Let ${\mathrm{H}}:\frac{x^{2}}{{\mathrm{a}}^{2}}-\frac{y^{2}}{{\ \mathrm{b}}^{2}}=1$ be a hyperbola whose eccentricity is equal to the length of semi-major axis of E , and whose length of latus rectum is equal to the length of minor axis of E . Then the distance between the foci of H is :

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3. JEE Main 2026 · 5 Apr · Shift 2 · Standard Equation

   Let the eccentricity e of a hyperbola satisfy the equation $6{\mathrm{e}}^{2}-11{\mathrm{e}}+3=0$. If the foci of the hyperbola are $(3,5)$ and $(3,-4)$, then the length of its latus rectum is :

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4. JEE Main 2026 · 4 Apr · Shift 2 · Standard Equation

   Let ${\mathrm{H}}:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is $\frac{8}{3}$. If the line $x=\alpha$ intersects the hyperbola H at the points A and B such that the area of the triangle AOB is $4\sqrt{15}$, where O is the origin, then $\alpha^{2}$ equals

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5. JEE Main 2026 · 2 Apr · Shift 2 · Rectangular Hyperbola

   Let O be the origin, and P and Q be two points on the rectangular hyperbola $xy=12$ such that the midpoint of the line segment PQ is $\left(\frac{1}{2},-\frac{1}{2}\right)$. Then the area of the triangle OPQ equals :

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6. JEE Main 2026 · 28 Jan · Shift 2 · Conjugate Hyperbola

   Let the ellipse $E:\frac{x^{2}}{144}+\frac{y^{2}}{169}=1$ and the hyperbola $H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}=-1$ have the same foci. If $e$ and $L$
   
   respectively denote the eccentricity and the length of the latus rectum of $H$, then the value of $24(e+L)$ is :

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7. JEE Main 2026 · 28 Jan · Shift 1 · Standard Equation

   For some $\theta\in \left(0,\frac{\pi}{2}\right)$, let the eccentricity and the length of the latus rectum of the hyperbola $x^{2}-y^{2}\sec^{2}\theta=8$ be $e_{1}$ and $l_{1}$, respectively, and let the eccentricity and the length of the latus rectum of the ellipse $x^{2}\sec^{2}\theta+y^{2}=6$ be $e_{2}$ and $l_{2}$, respectively. If $e_{1}^{2}=e_{2}^{2}\left(\sec^{2}\theta+1\right)$, then $\left(\frac{l_{1}l_{2}}{e_{1}e_{2}}\right)\tan^{2}\theta$ is equal to

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8. JEE Main 2026 · 23 Jan · Shift 2 · Standard Equation

   Let PQ be a chord of the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{b^{2}}=1$, perpendicular to the x -axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the eccentricity of the hyperbola is $\sqrt{3}$, then the area of the triangle OPQ is

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9. JEE Main 2026 · 23 Jan · Shift 1 · Standard Equation

   Let the domain of the function $f(x)=\log_{3}\log_{5}\log_{7}\left(9x-x^{2}-13\right)$ be the interval $({\mathrm{m}},{\mathrm{n}})$. Let the hyperbola $\frac{x^{2}}{{\mathrm{a}}^{2}}-\frac{y^{2}}{{\ \mathrm{b}}^{2}}=1$ have eccentricity $\frac{{\mathrm{n}}}{3}$ and the length of the latus rectum $\frac{8{\ \mathrm{m}}}{3}$. Then ${\mathrm{b}}^{2}-{\mathrm{a}}^{2}$ is equal to :

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10. JEE Main 2026 · 22 Jan · Shift 1 · Tangent and Normal

    If the line $\alpha x+2y=1$, where $\alpha\in {\mathbb{R}}$, does not meet the hyperbola $x^{2}-9y^{2}=9$, then a possible value of $\alpha$ is :

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11. JEE Main 2026 · 22 Jan · Shift 2 · Standard Equation

    Let ${\mathrm{P}}(10,2\sqrt{15})$ be a point on the hyperbola $\frac{x^{2}}{{\mathrm{a}}^{2}}-\frac{y^{2}}{{\ \mathrm{b}}^{2}}=1$, whose foci are S and ${\mathrm{S}}^{{'}}$. If the length of its latus rectum is 8 , then the square of the area of $\Delta{\mathrm{PSS}}^{{'}}$ is equal to :

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12. JEE Main 2026 · 21 Jan · Shift 1 · Standard Equation

    Let the foci of a hyperbola coincide with the foci of the ellipse $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$. If the eccentricity of the hyperbola is 5 , then the length of its latus rectum is :

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Sample questions from recent papers

The free PDF above has all 62 questions grouped by topic, with an answer key.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020