Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ axis. Accordingly, a = 3 and b = 2. Thus, the equation of the ellipse is x y x y 1 or 1. 2 2 2 2 2 2 3 2 9 4 Question 14: Find the equation for the ellipse that satisfies the given conditions: Ends of major axis ends of minor axis ( ±1, 0) Solution 14: Ends of major axis0, 5 , ends of minor axis (±1, 0) Here, the major axis is along the y-axis. x Therefore, the equation of the ellipse will be of the form b axis. Accordingly, a 5 = and b = 1. Thus, the equation of the ellipse is x y a 2 2 2 2 y x 1 or y 1 5 2 2 2 2 2 2 1 1 5 0, 5 1 , where a is the semi-major Question 15: Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0) Solution 15: Length of major axis = 26; foci = (±5, 0). Since the foci are on the x-axis, the major axis is along the x-axis. Therefore, the equation of the ellipse will be of the form axis. Accordingly, 2a = 26 ⇒ a = 13 and c = 5. It is known that a 2 = b 2 + c 2 . x a y b 2 2 2 2 1, where a is the semi-major 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 13 12 169 144 Question 16: Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6) Solution 16: Length of minor axis = 16; foci = (0, ±6). Since the foci are on the y-axis, the major axis is along 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, 2b = 16 ⇒ b = 8 and c = 6. It is known that a 2 = b 2 + c 2 . 2 2 2 a 8 6 64 36 100 a 100 10 Thus, the equation of the ellipse is x b 2 2 2 2 a 2 2 y x y 1 or 1 . 2 2 8 10 64 100 Question 17: Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4 Solution 17: Foci (±3, 0), a= 4 Since the foci are on the x-axis, the major axis is along the x-axis. Therefore, the equation of the ellipse will be of the form axis. Accordingly, c = 3 and a = 4. It is known that a 2 = b 2 + c 2 . x a y b 2 2 2 2 1, where a is the semi-major Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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