Which of the following points lies inside the ellipse $9 (x - 1)^{2} + 16 y^{2} = 25$

(\frac{1}{4}, \frac{3}{2})

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(\frac{1}{2}, \frac{5}{4})

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(\frac{3}{2}, 1)

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None of these

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Solution

The correct option is D $(\frac{1}{4}, \frac{3}{2})$
Ellipse is $9 (x - 1)^{2} + 16 y^{2} = 25$
$A) (\frac{1}{4}, \frac{3}{2}) 9 {(\frac{1}{4} - 1)}^{2} + 16 {(\frac{3}{2})}^{2} - 25 9 {(\frac{3}{4})}^{2} + 16 {(\frac{3}{2})}^{2} - 25 \frac{81}{16} + \frac{48}{16} - 25 = - 16.93 < 0$
hence it lies inside the ellipse.

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