Conic Sections Question 347
Question: hThe equation of the ellipse whose latus rectum is 8 and whose eccentricity is $ \frac{1}{\sqrt{2}} $ , referred to the principal axes of coordinates, is
[MP PET 1993]
Options:
A) $ \frac{x^{2}}{18}+\frac{y^{2}}{32}=1 $
B) $ \frac{x^{2}}{8}+\frac{y^{2}}{9}=1 $
C) $ \frac{x^{2}}{64}+\frac{y^{2}}{32}=1 $
D) $ \frac{x^{2}}{16}+\frac{y^{2}}{24}=1 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{2b^{2}}{a}=8, $
$ e=\frac{1}{\sqrt{2}} $
therefore $ a^{2}=64,b^{2}=32 $
Hence required equation of ellipse is $ \frac{x^{2}}{64}+\frac{y^{2}}{32}=1 $ .
BETA
