PrepWiser › Learn › Mathematics › EllipseEllipse — JEE Main PYQs & Practice Questions Ellipse is a Mathematics chapter in the JEE Main syllabus. This page brings together 100 previous-year and practice questions on Ellipse, organised into 5 topics: Standard Equation, Parametric Form, Auxiliary Circle, Tangent and Normal and Focal Chord. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Standard Equation If the midpoint of a chord of the ellipse x²/9+y²/4=1 is (√2, 4 / 3), and the length of… If x² + 9y² - 4x + 3 = 0, x, y ∈ R, then x and y respectively lie in the intervals : Let the line 2 x+3 y-k=0, k>0, intersect the x-axis and y-axis at the points A and B… If the length of the minor axis of an ellipse is equal to one fourth of the distance… Let the eccentricity of an ellipse x²/a²+y²/b²=1 is reciprocal to that of the hyperbola… Consider ellipses Eₖ: k x²+k² y²=1, k=1,2, …, 20. Let Cₖ be the circle which touches the… Let e₁ and e₂ be the eccentricities of the ellipse x²/b² + y²/25 = 1 and the hyperbola… The equation of the chord, of the ellipse x²/25+y²/16=1, whose mid-point is (3,1) is : Let an ellipse E:x²/a² + y²/b² = 1, a² > b², passes through ( √(3/2) ,1 ) and has… If the length of the latus rectum of the ellipse x²+4 y²+2 x+8 y-λ=0 is 4 , and l is the… Let a line L pass through the point of intersection of the lines b x+10 y-8=0 and 2 x-3… If the radius of the largest circle with centre (2,0) inscribed in the ellipse x²+4y²=36… Let the eccentricity of an ellipse x²/a² + y²/b² = 1, a > b, be 1/4. If this ellipse… If the length of the minor axis of an ellipse is equal to half of the distance between… Let C be the largest circle centred at (2, 0) and inscribed in the ellipse x²/36 + y²/16… Let e₁ and e₂ be the eccentricities of the ellipse, x²/25 + y²/b² = 1(b < 5) and the… A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes… The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and… Let the product of the focal distances of the point (√3, 1/2) on the ellipse… The centre of a circle C is at the centre of the ellipse E: x²/a²+y²/b²=1, a>b. Let C… Parametric Form Let S and S^' be the foci of the ellipse x²/25+y²/9=1 and P(α,β) be a point on the… Consider the parabola P:y²=4kx and the ellipse E:x²/a²+y²/b²=1. Let the line segment… An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at (5,-2). Then… Let (h,k) lie on the circle C:x²+y²=4 and the point (2h+1,3k+2) lie on an ellipse with… Let an ellipse x²/a²+y²/b²=1, a<b, pass through the point (4, 3) and have eccentricity… Let the length of the latus rectum of an ellipse x²/a²+y²/b²=1,(a>b), be 30 . If its… Let P(3 cos α,2 sin α),α≠ 0, be a point on the ellipse x²/9+y²/4=1,Q be a point on the… Let each of the two ellipses E₁:x²/a²+y²/b²=1,(a>b) and E₂:x²/A²+y²/B²=1,( A<B) have… Let a focus of the ellipse E:x²/a²+y²/b²=1 be S(4,0) and its eccentricity be 4/5. If the… Let x²/f(a²+7a+3)+y²/f(3a+15)=1 represent an ellipse with major axis along y-axis, where… Auxiliary Circle Tangent and Normal If the line α x+4y=√7, where α∈ R, touches the ellipse 3x²+4y²=1 at the point P in the… Let the tangents at the points P and Q on the ellipse x²/2+y²/4=1 meet at the point… Let the tangent and normal at the point (3 √3, 1) on the ellipse x²/36+y²/4=1 meet the… An angle of intersection of the curves, x²/a² + y²/b² = 1 and x² + y² = ab, a > b, is : If m is the slope of a common tangent to the curves x²/16 + y²/9 = 1 and x² + y² = 12… On the ellipse x²/8 + y²/4 = 1 let P be a point in the second quadrant such that the… A common tangent T to the curves C₁: x²/4+y²/9=1 and C₂: x²/42-y²/143=1 does not pass… If the maximum distance of normal to the ellipse x²/4+y²/b²=1, b < 2, from the origin is… The acute angle between the pair of tangents drawn to the ellipse 2 x²+3 y²=5 from the… Let x = 4 be a directrix to an ellipse whose centre is at the origin and its… The line x=8 is the directrix of the ellipse E:x²/a²+y²/b²=1 with the corresponding… If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of it… Let L be a tangent line to the parabola y² = 4x - 20 at (6, 2). If L is also a tangent… Let a circle of radius 4 be concentric to the ellipse 15 x²+19 y²=285. Then the common… Let θ be the acute angle between the tangents to the ellipse x²/9 + y²/1 = 1 and the… Let the line y = mx and the ellipse 2x² + y² = 1 intersect at a ponit P in the first… Let for two distinct values of p the lines y=x+p touch the ellipse E: x²/4²+y²/3²=1 at… If the curves, x²/a + y²/b = 1 and x²/c + y²/d = 1 intersect each other at an angle of… Let L be a common tangent line to the curves 4x² + 9y² = 36 and (2x)² + (2y)² = 31. Then… Let C be the circle x²+(y-1)²=2, E₁ and E₂ be two ellipses whose centres lie at the… Focal Chord More Mathematics chapters Frequently asked questions How many Ellipse questions are there for JEE Main? PrepWiser has 100 Ellipse questions for JEE Main, grouped into 5 topics such as Standard Equation, Parametric Form and Auxiliary Circle.
Are these Ellipse 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 Ellipse questions? Open any Ellipse question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.