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JEE Main PYQ + Theory | Prabhat Ranjan (Playlist):    • JEE Main PYQ + Theory | Prabhat Ranjan  

Ellipse (Part 3/3) JEE Main PYQ + Theory | Prabhat Ranjan

Ellipse Question 21-31 (Part 3/3) Class 11, 12 Mathematics Boards, JEE Main, JEE Advanced, IIT JEE Full course from basic JEE Main Question Practice JEE Main PYQ + Theory by Prabhat Ranjan for class 12, boards, IIT JEE 2025, JEE Main 2025, JEE Advanced 2025, IIT JEE 2026, JEE Main 2026, JEE Advanced 2026.

In "Ellipse (Part 3/3) JEE Main PYQ + Theory" by Prabhat Ranjan, Questions 21-31 of the ellipse section are explored for Class 11 and 12 students, with a focus on the mathematics relevant to JEE Main and Advanced for the years 2025 and 2026. This final section delves deeper into advanced problems concerning ellipses, including the focal properties, tangents, normals, and chord equations. The aim is to equip students with the necessary problem-solving techniques by solving previous year questions (PYQs) and connecting theory with practical applications. By mastering these problems, students will be well-prepared for conic section-related topics in the JEE exams, helping them achieve high scores in competitive tests like JEE Main 2024, JEE 2025, and beyond. The series highlights essential concepts from conic sections and emphasizes the importance of these in the mathematics portion of the exam, offering a valuable resource for exam success.

All these aspects have been covered by Prabhat Ranjan in full detail in his new YouTube video.

I am Prabhat Ranjan, currently pursuing B.Tech in Mechanical Engineering from NIT Jamshedpur.

Timeline:
00:00 Introduction
01:41 21) Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of pi/2 at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse E : x2/a2 +y2/b2 = 1, a2 greater than b2. If e is the eccentricity of the ellipse E, then the value of 1/e2 is equal to
17:32 22) If the ellipse x^2/a^2+y^2/b^2=1 meets the line x/7+y/2√6=1 on the X-axis and the line x/7-y/2√6=1 on the y-axis, then the eccentricity of the ellipse is
21:48 23) The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is
32:31 24) If the tangent at a point P on the parabola y2 = 3x is parallel to the line x + 2y = 1 and the tangents at the points Q and R on the ellipse x2/4 + y2/1 = 1 are perpendicular to the line x – y = 2, then the area of the triangle PQR is
41:24 25) Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, - 4), one focus at (4, -4) and one vertex at (5, -4). If mx - y = 4, m greater than 0 is a tangent to the ellipse E, then the value of 5m2 is equal to
47:22 26) If the minimum area of the triangle formed by a tangent to the ellipse x2/b2 + y2/4a2 =1 and the co-ordinate axis is kab, then k is equal to
53:27 27) If two tangents drawn from a point (a, ß) lying on the ellipse 25x2 + 4y2 = 1 to the parabola y2 = 4x are such that the slope of one tangent is four times the other, then the value of (10a +5)2 +(16ß2 +50)2 equals
01:05:26 28) If the length of the latus rectum of the ellipse x2 + 4y2 + 2x + 8y - lambda = 0 is 4, and l is the length of its
major axis, then lambda + l is equal to
01:12:32 29) Let S = {(x,y) belongs to NxN: 9(x-3)2 + 16(y-4)2 ≤ 144} and T = {(x,y) belongs to RxR: (x-7)2 + (y-4)2 ≤ 36}. The n(S∩T) is equal to
01:28:34 30) Let C be the largest circle centred at (2, 0) and inscribed in the ellipse x2/36 + y2/16 = 1. If (1, a) lies on C, then 10a2 is equal to
01:41:39 31) Let an ellipse with centre (1, 0) and latus rectum of length 1/2 have its major axis along x-axis. If its minor axis subtends an angle 60° at the foci, then the square of the sum of the lengths of its minor and major axes is equal to

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