Ratio of the greatest and least focal distances of a point on the ellipse $4 x^{2} + 9 y^{2} = 36$ is:

4 + \sqrt{5} : 4 - \sqrt{5}

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5 + \sqrt{5} : 4 - \sqrt{3}

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3 + \sqrt{5} : 3 - \sqrt{5}

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\sqrt{7} : 2

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Solution

The correct option is D $3 + \sqrt{5} : 3 - \sqrt{5}$
$e = \sqrt{1 - \frac{b^{2}}{a^{2}}} = \sqrt{1 - \frac{4}{9}} = \frac{\sqrt{5}}{3}$
$\frac{A S}{B S} = \frac{a + a e}{a - a e} = \frac{3 + \sqrt{5}}{3 - \sqrt{5}}$

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Similar questions

4 x^{2} + 9 y^{2} + 8 x + 36 y + 4 = 0

4 x^{2} + 9 y^{2} = 36

Two bodies A and B have masses in the ratio 9 : 4 and K.E in the ratio 36 : 25. Calculate ratio of their velocities.

4 x^{2} - 9 y^{2} = 36

4

(7, 2, 4)

A (2, 5, - 3), B (- 2, - 3, 5)

C (5, 3, - 3) .

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