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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 30 of 71
Marks: +1, -0
x216+y29\frac{x^2}{16}+\frac{y^2}{9} = 1
Solution:  
Given equation of ellipse is x216+y29\frac{x^2}{16}+\frac{y^2}{9} = 1 Clearly, 16 > 9
The equation of ellipse in standard form is x2a2+y2b2\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1
a2a^2 = 16 ⇒ a = 4 and b2b^2 = 9 ⇒ b = 3
We know that c = a2b2\sqrt{a^2-b^2} ⇒ c = 169\sqrt{16-9} = 7\sqrt{7}
∴ Coordinates of foci are (±c, 0) i.e. (± 7\sqrt{7} , 0)
Coordinates of vertices are (±a, 0) i.e. (±4, 0).
Length of major axis = 2a = 2 × 4 = 8
Length of minor axis = 2b = 2 × 3 = 6
Eccentricity (e) = ca\frac{c}{a} = 74\frac{\sqrt{7}}{4}
Length of latus rectum = 2b2a\frac{2b^2}{a} = 2×94\frac{2\times 9}{4} = 92\frac{9}{2}
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