PrepWiser › Learn › Mathematics › HyperbolaHyperbola — JEE Main PYQs & Practice Questions Hyperbola is a Mathematics chapter in the JEE Main syllabus. This page brings together 62 previous-year and practice questions on Hyperbola, organised into 4 topics: Standard Equation, Conjugate Hyperbola, Rectangular Hyperbola and Tangent and Normal. Most questions come with a step-by-step solution you can work through free in PrepWiser.
Download Hyperbola JEE Main PYQs as a free PDF
Revise this chapter: Revision notes · Formula sheet
Chapter weightage : how many questions each chapter had per shift in the 2024–26 papers.
Standard Equation Let H: -x²/a²+y²/b²=1 be the hyperbola, whose eccentricity is √3 and the length of the… Let H₁: x²/a²-y²/b²=1 and H₂:-x²/A²+y²/B²=1 be two hyperbolas having length of latus… Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus… Let the product of the focal distances of the point P(4,2 √3) on the hyperbola H… The locus of the centroid of the triangle formed by any point P on the hyperbola 16x² -… Let the foci of a hyperbola be (1,14) and (1,-12). If it passes through the point (1,6)… Let the foci and length of the latus rectum of an ellipse x²/a²+y²/b²=1, a>b b e( ± 5,0)… Let P be a point on the hyperbola H: x²/9-y²/4=1, in the first quadrant such that the… If the equation of the hyperbola with foci (4,2) and (8,2) is 3 x²-y²-α x+β y+γ=0, then… Let the foci of a hyperbola H coincide with the foci of the ellipse E… The length of the latus rectum and directrices of hyperbola with eccentricity e are 9… A hyperbola passes through the foci of the ellipse x²/25 + y²/16 = 1 and its transverse… For some θ∈ (0,π/2), let the eccentricity and the length of the latus rectum of the… Let the foci of a hyperbola coincide with the foci of the ellipse x²/36+y²/16=1. If the… A hyperbola having the transverse axis of length √2 has the same foci as that of the… Let PQ be a chord of the hyperbola x²/4-y²/b²=1, perpendicular to the x -axis such that… Let the sum of the focal distances of the point P(4,3) on the hyperbola H: x²/a²-y²/b²=1… Let Hₙ: x²/(1+n)-y²/(3+n)=1, n ∈ N. Let k be the smallest even value of n such that the… Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be… The eccentricity of an ellipse E with centre at the origin O is √3/2 and its directrices… Conjugate Hyperbola Rectangular Hyperbola Tangent and Normal Let the eccentricity of the hyperbola H:x²/a² - y²/b² = 1 be √(5/2) and length of its… Let the eccentricity of the hyperbola x²/a² - y²/b² = 1 be 5/4. If the equation of the… Let λ x - 2y = μ be a tangent to the hyperbola a²x² - y² = b². Then ( λ/a )² - ( μ/b )²… Let the tangent to the parabola y²=12 x at the point (3, α) be perpendicular to the line… If a hyperbola passes through the point P(10, 16) and it has vertices at (± 6, 0), then… Let the equation of two diameters of a circle x²+y²-2 x+2 f y+1=0 be 2 p x-y=1 and 2 x+p… A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola x²/4 - y²/2… Let P(3, 3) be a point on the hyperbola, x²/a² - y²/b² = 1. If the normal to it at P… Consider a hyperbola H : x² - 2y² = 4. Let the tangent at a point P(4, √6 ) meet the… Let the tangent drawn to the parabola y²=24 x at the point (α, β) is perpendicular to… The locus of the mid points of the chords of the hyperbola x² - y² = 4, which touch the… The vertices of a hyperbola H are (± 6, 0) and its eccentricity is √5/2. Let N be the… The locus of the midpoints of the chord of the circle, x² + y² = 25 which is tangent to… The normal to the hyperbola x²/a² - y²/9 = 1 at the point ( 8,3√3 ) on it passes through… Let P(x₀, y₀) be the point on the hyperbola 3 x²-4 y²=36, which is nearest to the line 3… The point P( - 2√6 ,√3 ) lies on the hyperbola x²/a² - y²/b² = 1 having eccentricity… The foci of a hyperbola are ( ± 2,0) and its eccentricity is 3/2. A tangent… Let a line L₁ be tangent to the hyperbola x²/16 - y²/4 = 1 and let L₂ be the line… Let m₁ and m₂ be the slopes of the tangents drawn from the point P(4,1) to the hyperbola… If the line α x+2y=1, where α∈ ℝ, does not meet the hyperbola x²-9y²=9, then a possible… More Mathematics chapters Frequently asked questions How many Hyperbola questions are there for JEE Main? PrepWiser has 62 Hyperbola questions for JEE Main, grouped into 4 topics such as Standard Equation, Conjugate Hyperbola and Rectangular Hyperbola.
Are these Hyperbola questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Hyperbola questions? Open any Hyperbola question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.