Conic Sections Question 299
Question: The equation of the ellipse whose vertices are $ (\pm 5,\ 0) $ and foci are $ (\pm 4,\ 0) $ is
Options:
A) $ 9x^{2}+25y^{2}=225 $
B) $ 25x^{2}+9y^{2}=225 $
C) $ 3x^{2}+4y^{2}=192 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Vertices $ (\pm 5,0)\equiv (\pm a,0) $
therefore $ a=5 $
Foci $ (\pm 4,0)\equiv (\pm ae,0) $
therefore $ e=\frac{4}{5} $ , $ b=(5)( \frac{3}{5} )=3 $
Hence equation is $ \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 $ i.e., $ 9x^{2}+25y^{2}=225 $ .
BETA
