Conic Sections Question 386
Question: The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is
Options:
A) $ 5x^{2}-9y^{2}=180 $
B) $ 9x^{2}+5y^{2}=180 $
C) $ x^{2}+9y^{2}=180 $
D) $ 5x^{2}+9y^{2}=180 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ 2ae=8,\frac{2a}{e}=18 $
therefore $ a=\sqrt{4\times 9}=6 $
$ e=\frac{2}{3}, $
$ b=6\sqrt{1-\frac{4}{9}}=\frac{6}{3}\sqrt{5}=2\sqrt{5} $
Hence the required equation is $ \frac{x^{2}}{36}+\frac{y^{2}}{20}=1 $
i.e., $ 5x^{2}+9y^{2}=180 $ .
BETA
