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Question: Eccentricity of ellipse \(\frac{x^{2}}{a^{2}}\) + \(\frac{y^{2}}{b^{2}}\) = 1 if it passes through p...

Eccentricity of ellipse x2a2\frac{x^{2}}{a^{2}} + y2b2\frac{y^{2}}{b^{2}} = 1 if it passes through points (9, 5) & (12, 4) is :

A

34\sqrt{\frac{3}{4}}

B

45\sqrt{\frac{4}{5}}

C

56\sqrt{\frac{5}{6}}

D

67\sqrt{\frac{6}{7}}

Answer

67\sqrt{\frac{6}{7}}

Explanation

Solution

We have 81a2\frac{81}{a^{2}} + 25b2\frac{25}{b^{2}} = 1 ………(1)

144a2\frac{144}{a^{2}} + 16b2\frac{16}{b^{2}} = 1……...(2)

from (2) – (1)

63a2\frac{63}{a^{2}} – 9b2\frac{9}{b^{2}} = 0 ̃ b2a2\frac{b^{2}}{a^{2}} = 17\frac{1}{7}

e = 1–17\sqrt{1–\frac{1}{7}} = 67\sqrt{\frac{6}{7}}