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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 47 of 71
Marks: +1, -0
Major axis on the x-axis and passes through the points (4, 3) and (6, 2).
Solution:  
Since the major axis is along the x-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 point (4, 3)
16a2+9b2\frac{16}{a^2}+\frac{9}{b^2} = 1 ... (i)
Also, the ellipse passes through point (6, 2)
36a2+4b2\frac{36}{a^2}+\frac{4}{b^2} = 1 ... (ii)
Solving (i) and (ii), we get a2a^2 = 52 and b2b^2 = 13
Hence the required equation of ellipse is x252+y213\frac{x^2}{52}+\frac{y^2}{13} = 1.
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