Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ 4 b 3 2 2 2 2 16 b 9 2 b 16 9 7 Thus, the equation of the ellipse is 2 2 x y 1 . 16 7 Question 18: Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis. Solution 18: It is given that b= 3, c = 4, centre at the origin; foci on the x axis. 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, b = 3, c= 4. It is known that a 2 = b 2 + c 2 . 2 2 2 a 3 4 916 25 a 5 Thus, the equation of the ellipse is x x a 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 19: Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6). Solution 19: Since the centre is at (0, 0) and the major axis is on the y-axis, the equation of the ellipse will be of the form 2 2 x y 1 1 2 2 a b Where, a is the semi-major axis The ellipse passes through points (3, 2) and (1, 6). Hence, 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 ______________________________________________________________________________ 9 4 1 2 2 b a 2 1 36 2 2 1 b a 3 On solving equations (2) and (3), we obtain b 2 = 10 and a 2 = 40. Thus, the equation of the ellipse is x 2 2 2 10 + 40 y 1 or 4x 2 + y2 = 40. Question 20: Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2). Solution 20: Since the major axis is on the x-axis, the equation of the ellipse will be of the form 2 2 x y 1 2 2 1 a b Where, a is the semi-major axis The ellipse passes through points (4, 3) and (6, 2). Hence, 16 9 1 2 2 2 a b 36 4 1 2 2 3 a b On solving equations (2) and (3), we obtain a 2 = 52 and b 2 = 13. 2 2 x y Thus, the equation of the ellipse is 1or x 2 + 4y 2 = 52. 52 13 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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