10 JEE Main 2023 Ellipse previous-year questions with verified answers and step-by-step solutions.
These are the JEE Main 2023 previous-year questions from the Ellipse chapter of Mathematics. Each links to a full solution with a verified answer key. To see the whole chapter across all years, visit the Ellipse chapter hub.
Let an ellipse with centre 1 ,   0 and latus rectum of length 1 2 have its major axis along x-axis. If its minor a…
Let the ellipse E : x 2 + 9 y 2 = 9 intersect the positive x - and y -axes at the points A and B respectively. Let the…
If the tangent at a point P on the parabola y 2 = 3 x is parallel to the line x + 2 y = 1 and the tangents at the point…
Let C be the largest circle centred at 2 , 0 and inscribed in the ellipse x 2 36 + y 2 16 = 1 . If 1 , α lies on C…
Let P 2 3 7 ,   6 7 ,   Q ,   R and S be four points on the ellipse 9 x 2 + 4 y 2 = 36 . Let P Q and R S…
The line x = 8 is the directrix of the ellipse E : x 2 a 2 + y 2 b 2 = 1 with the corresponding focus 2 , 0 . If the ta…
Let a tangent to the curve 9 x 2 + 16 y 2 = 144 intersect the coordinate axes at the points A and B . Then, the minimum…
Let a circle of radius 4 be concentric to the ellipse 15 x 2 + 19 y 2 = 285 . Then the common tangents are inclined to…
If the radius of the largest circle with centre ( 2 ,   0 ) inscribed in the ellipse x 2 + 4 y 2 = 36 is r , then…
Let the tangent and normal at the point 3 3 , 1 on the ellipse x 2 36 + y 2 4 = 1 meet the y - axis at the points A and…