Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ c 5 Eccentricity, e= a 3 Length of latus rectum 2 2b 24 8 a 3 3 Question 10: Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0) Solution 10: Vertices (±5, 0), foci (±4, 0) Here, the vertices are on the x-axis. x Therefore, the equation of the ellipse will be of the form a axis. Accordingly, a = 5 and c = 4. It is known that a 2 = b 2 + c 2 . 2 2 2 5 b 4 2 25 b 16 2 b 25 16 b 9 3 Thus, the equation of the ellipse is x 2 2 2 2 2 2 5 3 25 9 y b 2 2 2 2 y x y 1 or 1 1 , where a is the semi-major Question **11**: Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5) Solution **11**: Vertices (0, ±13), foci (0, ±5) Here, the vertices are on the y-axis. 2 2 x y Therefore, the equation of the ellipse will be of the form 1 , where a is the semi-major axis. Accordingly, a = 13 and c = 5. It is known that a 2 = b 2 + c 2 . b a 2 2 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 ______________________________________________________________________________ 13 b 5 2 2 2 2 169 b 25 2 b 169 25 b 144 12 Thus, the equation of the ellipse is x y x y 1 or 1. 2 2 2 2 2 2 12 13 144 169 Question 12: Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0) Solution 12: Vertices (±6, 0), foci ( ±4, 0) Here, the vertices are on the x-axis. Therefore, the equation of the ellipse will be of the form axis. Accordingly, a = 6, c= 4. It is known as a 2 = b 2 + c 2 . 2 2 2 6 b 4 2 36 b 16 2 b b 36 16 20 Thus, the equation of the ellipse is x x a y b 2 2 2 2 y x 1 or y 1 20 2 2 2 2 2 2 6 36 20 1 , where a is the semi-major Question 13: Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2) Solution 13: Ends of major axis (±3, 0), ends of minor axis (0, ±2) Here, the major axis is along the x-axis. Therefore, the equation of the ellipse will be of the form 2 2 2 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. x a y 1, where a is the semi-major b

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