The sum of the focal distances from any point on the ellipse $9x^2 + 16y^2 = 144$ is
A32
B18
C16
D8
Answer & Solution
Correct answer: D. 8
Write the ellipse in standard form: $$\frac{x^2}{16}+\frac{y^2}{9}=1.$$ Hence the semi-major axis is $a=4$. For any point on an ellipse, the sum of distances from the two foci is $2a$. Therefore the required sum is $$2a=8.$$ Comparing with the options, the matching choice is $8$.
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