Question
Download Solution PDFEccentricity of ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\mathbf{1}\), if it passes through point (9, 5) and (12, 4) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Given \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\mathbf{1}\)
At (9, 5)
\(\frac{81}{a^2} + \frac{25}{b^2} = 1\) ......(1)
At (12,4)
\(\frac{144}{a^2} + \frac{16}{b^2} = 1\) .......(2)
From eq. (2) - eq. (1):
\(\frac{63}{a^2} - \frac{9}{b^2} = 0\)
⇒ \(\frac{b^2}{a^2} = \frac{1}{7}\)
⇒ \(\frac{b}{a} = \frac{1}{\sqrt{7}}\)
e = \(\sqrt{1 - \frac{b^2}{a^2}}\) = \(\sqrt{1 - \frac{1}{7}}\) = \(\sqrt{\frac{6}{7}}\)
Hence option 4 is correct
Last updated on Jul 3, 2025
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