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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 37 of 71
Marks: +1, -0
Vertices (±5, 0), foci (±4, 0)
Solution:  
Clearly, the foci (±4, 0) lie on x-axis.
∴ The equation of ellipse in standard form is x2a2+y2b2\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1
Now vertices are (±5, 0) ⇒ a = 5, foci are (±4, 0) ⇒ c = 4
Also, we know that c2c^2 = a2b2a^2 - b^2
(4)2(4)^2 = (5)2b2(5)^2 - b^2b2b^2 = 25 – 16 = 9.
Hence the required equation of ellipse is x225+y29\frac{x^2}{25}+\frac{y^2}{9} = 1
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