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Q.

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse $9 y^{2} + x^{2} = 9$ meets its auxiliary circle at M. If $Δ$ denotes the area of $Δ A M O$ , then $20 Δ$ is equal to

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a

48

b

36

c

54

d

64

answer is B.

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Detailed Solution

Equation of AM is $x + 3 y - 3 = 0$
Perpendicular distance from origin $= \frac{3}{\sqrt{10}}$
Question Image
Length of AM $= 2 \sqrt{g - \frac{g}{10}} = \frac{18}{\sqrt{10}}$
Area $= \frac{1}{2} \times \frac{18}{\sqrt{10}} \times \frac{3}{\sqrt{10}} = \frac{27}{10}$ sq units

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