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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 46 of 71
Marks: +1, -0
Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6)
Solution:  
Since the major axis is along y-axis.
∴ The equation of ellipse in standard form is x2a2+y2b2\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1
Since the ellipse passes through the point (3, 2)
9b2+4a2\frac{9}{b^2}+\frac{4}{a^2} = 1 ... (i)
Also, the ellipse passes through point (1, 6)
1b2+36a2\frac{1}{b^2}+\frac{36}{a^2} = 1 ... (ii)
Solving (i) and (ii), we get a2a^2 = 40 and b2b^2 = 10
Hence the required equation of ellipse is x210+y240\frac{x^2}{10}+\frac{y^2}{40} = 1.
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