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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 43 of 71
Marks: +1, -0
Length of minor axis 16, foci (0, ±6)
Solution:  
Since the foci (0, ±6) lie on y-axis.
∴ The equation of ellipse in standard form is x2a2+y2b2\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1
Now, length of minor axis 2b = 16 ⇒ b = 8, Foci are (0, ±6) ⇒ c = 6
we know that c2c^2 = a2b2a^2 - b^2
(6)2(6)^2 = a2(8)2a^2 - (8)^2a2a^2 = 36 + 64 = 100.
Hence the required equation of ellipse is x264+y2100\frac{x^2}{64}+\frac{y^2}{100} = 1.
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