Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ The coordinates of the foci are 0, 5 3 . The coordinates of the vertices are (0, ±10). Length of major axis = 2a= 20 Length of minor axis = 2b= 10 c 5 3 3 Eccentricity, e = a 10 2 Length of latus rectum 2 2b 225 5 a 10 Question 5: Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the 2 2 x y eccentricity and the length of the latus rectum of the ellipse 1 49 36 Solution 5: 2 2 2 2 x y x y The given equation is 1or 1 2 2 49 36 7 6 2 2 x y Here, the denominator of is greater than the denominator of . 49 36 Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis. 2 2 x y On comparing the given equation with 1 , we obtain a = 7 and b = 6. 2 2 a b 2 2 c a b 49 36 13 Therefore, The coordinates of the foci are 13,0 The coordinates of the vertices are ( ±7, 0). Length of major axis = 2a= 14 Length of minor axis = 2b= 12 c 13 Eccentricity, e = a 7 2 2b 236 72 Length of latus rectum = a 7 7 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Question 6: Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse Solution 6: The given equation is 2 2 2 2 x y x y 1or 100 400 10 20 1 2 2 2 2 x y 1 100 400 2 x . Here, the denominator of is greater than the denominator of 100 Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis. On comparing the given equation with, x b y we obtain b = 10 and a = 20. a 2 2 1 2 2 2 2 c a b 400 100 300 10 3 Therefore, The coordinates of the foci are 0, 10 3. The coordinates of the vertices are (0, ±20) Length of major axis = 2a= 40 Length of minor axis = 2b= 20 c 10 3 3 Eccentricity, e= a 20 2 Length of latus rectum 2 2b 2100 10 a 20 Question 7: Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36x 2 + 4y 2 = 144 Solution 7: The given equation is 36x2+ 4y2= 144. It can be written as 2 2 36x 4y **11**4 2 2 x y Or, 1 4 36 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 15 - Statistics Ma

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