JEE MAIN Hyperbola Previous Year Question Paper and Solution with PDF

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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Hyperbola PYQ

Qus : 1 JEE MAIN PYQ

Consider a hyperbola $\text{H}$ having centre at the origin and foci on the x-axis. Let $C_1$ be the circle touching the hyperbola $\text{H}$ and having the centre at the origin. Let $C_2$ be the circle touching the hyperbola $\text{H}$ at its vertex and having the centre at one of its foci. If areas (in sq units) of $C_1$ and $C_2$ are $36\pi$ and $4\pi$, respectively, then the length (in units) of latus rectum of $\text{H}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let the matrix $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$ satisfy $A^n=A^{n-2}+A^2-I$ for $n \geqslant 3$. Then the sum of all the elements of $\mathrm{A}^{50}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Evening Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

Let $S = \{(x, y) \in \mathbb{R}^2 : \dfrac{y^2}{1 + r} - \dfrac{x^2}{1 - r} = 1 ; \, r \neq \pm 1 \}$. Then $S$ represents :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Evening Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

If the line $x-1=0$ is a directrix of the hyperbola $kx^{2}-y^{2}=6$, then the hyperbola passes through the point:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

If a hyperbola has length of its conjugate axis equal to $5$ and the distance between its foci is $13$, then the eccentricity of the hyperbola is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

Qus : 6 JEE MAIN PYQ

If the vertices of a hyperbola are at $(-2,0)$ and $(2,0)$ and one of its foci is at $(-3,0)$, then which one of the following points does not lie on this hyperbola?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Morning Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

Let $H:\dfrac{-x^2}{a^2}+\dfrac{y^2}{b^2}=1$ be the hyperbola whose eccentricity is $\sqrt{3}$ and the length of the latus rectum is $4\sqrt{3}$. Suppose the point $(\alpha,6)$, $\alpha>0$, lies on $H$. If $\beta$ is the product of the focal distances of the point $(\alpha,6)$, then $\alpha^2+\beta$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

A hyperbola having the transverse axis of length $\sqrt 2 $ has the same foci as that of the ellipse 3x² + 4y² = 12, then this hyperbola does notpass through which of the following points?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Morning) PYQ

Solution

Qus : 9 JEE MAIN PYQ

Let $P$ be a point on the hyperbola $H:\ \dfrac{x^2}{9}-\dfrac{y^2}{4}=1$, in the first quadrant, such that the area of the triangle formed by $P$ and the two foci of $H$ is $2\sqrt{13}$. Then, the square of the distance of $P$ from the origin is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Evening Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16x^{2}-y^{2}+64x+4y+44=0$. Then the area of the region above the parabola $x^{2}=y+4$, below the transverse axis $T$ and on the right of the conjugate axis $C$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Evening Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

Let one focus of the hyperbola $\textbf{H}: \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ be at $(\sqrt{10}, 0)$ and the corresponding directrix be $x = \dfrac{9}{\sqrt{10}}$. If $e$ and $l$ respectively are the eccentricity and the length of the latus rectum of $\textbf{H}$, then $9(e^2 + l)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Morning Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola ${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$. Let e' and l' respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If ${e^2} = {{11} \over {14}}l$ and ${\left( {e'} \right)^2} = {{11} \over 8}l'$, then the value of $77a + 44b$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Evening Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $\displaystyle E:\ \frac{(x-1)^{2}}{100}+\frac{(y-1)^{2}}{75}=1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $H$ is $\alpha$ and the length of its conjugate axis is $\beta$, then $3\alpha^{2}+2\beta^{2}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Evening Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let e₁ and e₂ be the eccentricities of theellipse, ${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$(b < 5) and the hyperbola, ${{{x^2}} \over {16}} - {{{y^2}} \over {{b^2}}} = 1$ respectively satisfying e₁e₂ = 1. If $\alpha $ and $\beta $ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair ($\alpha $, $\beta $) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Evening) PYQ

Solution

Qus : 15 JEE MAIN PYQ

The eccentricity of the hyperbola whose length of the latus rectum is equal to $8$ and the length of its conjugate axis is equal to half of the distance between its foci, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 16 JEE MAIN PYQ

Let $0<\theta<\frac{\pi}{2}$. If the eccentricity of the hyperbola $\dfrac{x^2}{\cos^2\theta}-\dfrac{y^2}{\sin^2\theta}=1$ is greater than $2$, then the length of its latus rectum lies in the interval:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Morning Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Let $a$ and $b$ respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^{2} - 18e + 5 = 0$. If $S(5,0)$ is a focus and $5x = 9$ is the corresponding directrix of this hyperbola, then $a^{2} - b^{2}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ along the $x$-axis. Then the eccentricity of the hyperbola is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2\sqrt{3})$ is $5x=4\sqrt{5}$ and its eccentricity is $e$, then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Morning Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

The locus of the centroid of the triangle formed by any point P on the hyperbola $16{x^2} - 9{y^2} + 32x + 36y - 164 = 0$, and its foci is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Morning Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

If $5x+9=0$ is the directrix of the hyperbola $16x^{2}-9y^{2}=144$, then its corresponding focus is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

Let the foci of the ellipse $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{7}=1$ and the hyperbola $\dfrac{x^{2}}{144}-\dfrac{y^{2}}{\alpha}=\dfrac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Evening Shift) PYQ

Solution

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