JEE Advanced Conic Sections — previous year questions

69 questions from 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007.

• Let T be the tangent to the parabola y² = 16x at the point (64, 32). Let L be the tangent to the same…2026JEE Advanced
• Match each entry in List-I to the correct entry in List-II and choose the correct option. | List-I | List-II…2026JEE Advanced
• Let S denote the locus of the point of intersection of the pair of lines 4x - 3y = 12α, 4α x + 3α y = 12,…2025JEE Advanced
• Let P(x₁, y₁) and Q(x₂, y₂) be two distinct points on the ellipse x²/9 + y²/4 = 1 such that y₁ > 0 and y₂ >…2025JEE Advanced
• A normal with slope 1/√6 is drawn from the point (0,-α) to the parabola x²=-4ay, where a>0. Let L be the line…2024JEE Advanced
• Let A₁, B₁, C₁ be three points in the xy-plane. Suppose that the lines A₁C₁ and B₁C₁ are tangents to the…2024JEE Advanced
• Consider the ellipse x²/9 + y²/4 = 1. Let S(p, q) be a point in the first quadrant such that p²/9 + q²/4 > 1.…2024JEE Advanced
• Consider the ellipse E given by x²/18 + y²/12 = 1. Let H be the hyperbola whose eccentricity is the…2024JEE Advanced
• Let A₁, A₂, A₃, ......... A₈ be the vertices of a regular octagon that lie on a circle of radius 2. Let P be…2023JEE Advanced
• Let C₁ be the circle of radius 1 with center at the origin. Let C₂ be the circle of radius r with center at…2023JEE Advanced
• Let P be a point on the parabola y²=4ax, where a>0. The normal to the parabola at P meets the x-axis at a…2023JEE Advanced
• Let T₁ and T₂ be two distinct common tangents to the ellipse E:x²/6+y²/3=1 and the parabola P:y²=12x. Suppose…2023JEE Advanced
• Let ABC be the triangle with AB = 1, AC = 3 and ∠ BAC = π/2. If a circle of radius r > 0 touches the sides…2022JEE Advanced
• Let G be a circle of radius R > 0. Let G₁, G₂, …, Gₙ be n circles of equal radius r > 0. Suppose each of the…2022JEE Advanced
• Consider the parabola y² = 4x. Let S be the focus of the parabola. A pair of tangents drawn to the parabola…2022JEE Advanced
• Consider the ellipse x²/4 + y²/3 = 1. Let H(α, 0), 0 < α < 2, be a point. A straight line drawn through H…2022JEE Advanced
• Consider the hyperbola x²/100 - y²/64 = 1 with foci at S and S₁, where S lies on the positive x-axis. Let P…2022JEE Advanced
• Consider a triangle Δ whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of Δ…2021JEE Advanced
• For any complex number w = c + id, let arg(w) ∈ (-π, π], where i = √(-1). Let α and β be real numbers such…2021JEE Advanced
• Let E denote the parabola y² = 8x. Let P = (-2, 4), and let Q and Q' be two distinct points on E such that…2021JEE Advanced
• Let E be the ellipse x²/16 + y²/9 = 1. For any three distinct points P, Q and Q' on E, let M(P, Q) be the…2021JEE Advanced
• Let O be the centre of the circle x^2 + y^2 = r^2, where r > sqrt(5)/2. Suppose PQ is a chord of this circle…2020JEE Advanced
• Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that…2020JEE Advanced
• A line y = mx + 1 intersects the circle (x - 3)² + (y + 2)² = 25 at the points P and Q. If the midpoint of…2019JEE Advanced
• Let the point B be the reflection of the point A(2,3) with respect to the line 8x-6y-23=0. Let Γ_A and Γ_B be…2019JEE Advanced
• Let RS be the diameter of the circle x^2 + y^2 = 1, where S is the point (1, 0). Let P be a variable point…2019JEE Advanced
• Consider two straight lines, each of which is tangent to both the circle x² + y² = 1/2 and the parabola y² =…2018JEE Advanced
• Let H : x²/a² - y²/b² = 1, where a > b > 0, be a hyperbola in the xy-plane whose conjugate axis LM subtends…2018JEE Advanced
• For how many values of p, the circle x²+y²+2x+4y-p=0 and the coordinate axes have exactly three common points?2017JEE Advanced
• If a chord, which is not a tangent, of the parabola y^2 = 16x has the equation 2x + y = p, and midpoint (h,…2017JEE Advanced
• If 2x - y + 1 = 0 is a tangent to the hyperbola x²/a² - y²/16 = 1, then which of the following cannot be…2017JEE Advanced
• Let P be the point on the parabola y² = 4x which is at the shortest distance from the center S of the circle…2016JEE Advanced
• The circle C_1 : x^2 + y^2 = 3, with centre at O, intersects the parabola x^2 = 2y at the point P in the…2016JEE Advanced
• Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x + y + 4 = 0. If A and…2015JEE Advanced
• If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents to the circle…2015JEE Advanced
• Let P and Q be distinct points on the parabola y² = 2x such that a circle with PQ as diameter passes through…2015JEE Advanced
• Suppose that the foci of the ellipse x²/9+y²/5=1 are (f₁,0) and (f₂,0) where f₁>0 and f₂<0. Let P₁ and P₂ be…2015JEE Advanced
• Let E₁ and E₂ be two ellipses whose centers are at the origin. The major axes of E₁ and E₂ lie along the…2015JEE Advanced
• Consider the hyperbola H: x² - y² = 1 and a circle S with center N(x₂, 0). Suppose that H and S touch each…2015JEE Advanced
• The common tangents to the circle x² + y² = 2 and the parabola y² = 8x touch the circle at the points P, Q…2014JEE Advanced
• A circle S passes through the point (0, 1) and is orthogonal to the circles (x-1)²+y²=16 and x²+y²=1. Then…2014JEE Advanced
• Let the straight line y = 2x touch a circle with center (0, α), α > 0, and radius r at a point A_1. Let B_1…2014JEE Advanced
• Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 2√7 on y-axis is…2013JEE Advanced
• A vertical line passing through the point (h, 0) intersects the ellipse x²/4 + y²/3 = 1 at the points P and…2013JEE Advanced
• The ellipse E₁: x²/9 + y²/4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate…2012JEE Advanced
• Tangents are drawn to the hyperbola x²/9 - y²/4 = 1, parallel to the straight line 2x - y = 1. The points of…2012JEE Advanced
• The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.2011JEE Advanced
• The straight line 2x - 3y = 1 divides the circular region x^2 + y^2 <= 6 into two parts. If S = {(2, 3/4),…2011JEE Advanced
• Let (x, y) be any point on the parabola y² = 4x. Let P be the point that divides the line segment from (0, 0)…2011JEE Advanced
• Consider the parabola y² = 8x. Let Δ₁ be the area of the triangle formed by the end points of its latus…2011JEE Advanced
• Let L be a normal to the parabola y²=4x. If L passes through the point (9, 6), then L is given by2011JEE Advanced
• Let the eccentricity of the hyperbola x²/a² - y²/b² = 1 be reciprocal to that of the ellipse x² + 4y² = 4. If…2011JEE Advanced
• Let A and B be two distinct points on the parabola y^2 = 4x. If the axis of the parabola touches a circle of…2010JEE Advanced
• The line 2x + y = 1 is tangent to the hyperbola x²/a² - y²/b² = 1. If this line passes through the point of…2010JEE Advanced
• Tangents drawn from the point P(1, 8) to the circle x² + y² - 6x - 4y - 11 = 0 touch the circle at the points…2009JEE Advanced
• The centres of two circles C₁ and C₂ each of unit radius are at a distance of 6 units from each other. Let P…2009JEE Advanced
• The tangent PT and the normal PN to the parabola y² = 4ax at a point P on it meet its axis at points T and N,…2009JEE Advanced
• The normal at a point P on the ellipse x² + 4y² = 16 meets the x-axis at Q. If M is the mid point of the line…2009JEE Advanced
• The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse…2009JEE Advanced
• In a triangle ABC with fixed base BC, the vertex A moves such that cos B + cos C = 4sin²A/2. If a, b and c…2009JEE Advanced
• The locus of the orthocentre of the triangle formed by the lines (1+p)x - py + p(1+p) = 0, (1+q)x - qy +…2009JEE Advanced
• An ellipse intersects the hyperbola 2x² - 2y² = 1 orthogonally. The eccentricity of the ellipse is reciprocal…2009JEE Advanced
• Consider L₁ : 2x + 3y + p - 3 = 0 L₂ : 2x + 3y + p + 3 = 0 where p is a real number, and C : x² + y² + 6x -…2008JEE Advanced
• Let P(x₁, y₁) and Q(x₂, y₂), y₁ < 0, y₂ < 0, be the end points of the latus rectum of the ellipse x² + 4y² =…2008JEE Advanced
• Consider a branch of the hyperbola x² - 2y² - 2√2x - 4√2y - 6 = 0 with vertex at the point A. Let B be one of…2008JEE Advanced
• Let a and b be non-zero real numbers. Then, the equation (ax² + by² + c)(x² - 5xy + 6y²) = 0 represents2008JEE Advanced
• Tangents are drawn from the point (17, 7) to the circle x² + y² = 169. STATEMENT-1: The tangents are mutually…2007JEE Advanced
• STATEMENT-1: The curve y = (-x²)/2 + x + 1 is symmetric with respect to the line x = 1. because STATEMENT-2:…2007JEE Advanced
• A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x² + 4y² = 12. Then…2007JEE Advanced

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