Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Let AB intersect the x-axis at point C. Let OC = k From the equation of the given parabola, we have 2 y 4ak y 2 ak ∴The respective coordinates of points A and B are k,2 ak ,and k,-2 ak AB = CA + CB = 2 ak + 2 ak = 4 ak Since OAB is an equilateral triangle, OA 2 = AB 2 . 2 4 2 2 2 k ak ak 2 k 12ak k 12a 2 k 4ak 16ak 2 AB 4 ak 4 a12a 4 12a 8 3a Thus, the side of the equilateral triangle inscribed in parabola y 2 = 4 ax is 8 3a Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ Exercise 12.1 Book Name: **NCERT** Solutions Question 1: A point is on the x-axis. What are its y-coordinates and z-coordinates? Solution 1: If a point is on the x-axis, then its y-coordinates and z-coordinates are zero. Question 2: A point is in the XZ-plane. What can you say about its y-coordinate? Solution 2: If a point is in the XZ plane, then its y-coordinate is zero. Question 3: Name the octants in which the following points lie: (1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7) Solution 3: The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I. The x-coordinate, y-coordinate, and z-coordinate of point (4, -2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV. The x-coordinate, y-coordinate, and z-coordinate of point (4, -2, -5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII. The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, -5) are positive, positive, and negative respectively. Therefore, this point lies in octant V. The x-coordinate, y-coordinate, and z-coordinate of point (-4, 2, -5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI. The x-coordinate, y-coordinate, and z-coordinate of point (-4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II. The x-coordinate, y-coordinate, and z-coordinate of point (-3, -1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III. The x-coordinate, y-coordinate, and z-coordinate of point (2, -4, -7) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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