Position of a point $(3, - 4))$ with respect to the ellipse $16 x^{2} + 9 y^{2} = 144$ lies

outside

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inside

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None of the above

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Solution

The correct option is A outside
Given equation is $16 x^{2} + 9 y^{2} = 144$
$f (x, y) = 16 x^{2} + 9 y^{2} - 144 f (3, - 4) = 16 {(3)}^{2} + 9 (- 4)^{2} - 144 f (3, - 4) = 144 + 144 - 144 f (3, - 4) = 144 f (3, - 4) > 0$
So, the point lies outside the ellipse.
Option A is correct.

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