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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 44 of 71
Marks: +1, -0
Foci (±3, 0), a = 4
Solution:  
Since the foci (±3, 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, foci are (±3, 0) ⇒ c = 3
We know that c2c^2 = a2b2a^2 - b^2
(3)2(3)^2 = (4)2b2(4)^2 - b^2b2b^2 = 16 – 9 = 7.
Hence the required equation of ellipse is x216+y27\frac{x^2}{16}+\frac{y^2}{7} = 1.
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