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Question
The sum of the focal distances of any point on the ellipse 9x2 + 16y2 = 144 is
Options
32
18
16
8
Solution
8
\[ {9x}^2 {+ 16y}^2 = 144 \]
\[ \Rightarrow \frac{x^2}{16} + \frac{y^2}{9} = 1\]
\[\text{ Here, }a=4\text{ and }b=3\]
The sum of the focal distances of any point on an ellipse is constant and equal to the length of the major axis of the ellipse.
i . e . sum of the focal distances of any point on an ellipse = 2a
\[ = 2 \times 4\]
\[ = 8\]
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