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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 39 of 71
Marks: +1, -0
Vertices (±6, 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 (± 6, 0) ⇒ a = 6, foci are (± 4, 0) ⇒ c = 4
Also, we know that c2c^2 = a2b2a^2 - b^2
(4)2(4)^2 = (6)2b2(6)^2 - b^2b2b^2 = 36 – 16 = 20.
Hence, the required equation of ellipse is x236+y220\frac{x^2}{36} + \frac{y^2}{20} = 1.
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