Conic Sections Question 439
Question: The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of co-ordinates is
Options:
A) $ 3x^{2}-y^{2}=3 $
B) $ x^{2}-3y^{2}=3 $
C) $ 3x^{2}-y^{2}=9 $
D) $ x^{2}-3y^{2}=9 $
Show Answer
Answer:
Correct Answer: C
Solution:
According to given conditions, $ 2ae=2.2a $ or $ \sqrt{{{(x-2)}^{2}}+y^{2}}=4-\sqrt{{{(x-2)}^{2}}+y^{2}} $ and $ A\equiv (0,0);B\equiv (4a,4a) $ .
Hence, $ a=\frac{3}{\sqrt{3}}=\sqrt{3} $
Therefore, equation is $ \frac{x^{2}}{3}-\frac{y^{2}}{9}=1 $ i.e., $ 3x^{2}-y^{2}=9 $ .
BETA
