Conic Sections Question 433
Question: The length of transverse axis of the parabola $ 3x^{2}-4y^{2}=32 $ is
[Karnataka CET 2001]
Options:
A) $ \frac{8\sqrt{2}}{\sqrt{3}} $
B) $ \frac{16\sqrt{2}}{\sqrt{3}} $
C) $ \frac{3}{32} $
D) $ \frac{64}{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
The given equation may be written as $ \frac{x^{2}}{32/2}-\frac{y^{2}}{8}=1 $ or $ \frac{x^{2}}{{{( 4\sqrt{2}/\sqrt{3} )}^{2}}}-\frac{y^{2}}{{{(2\sqrt{2})}^{2}}}=1 $ . Comparing the given equation with $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ , we get $ a^{2}={{( \frac{4\sqrt{2}}{\sqrt{3}} )}^{2}} $ or $ a=\frac{4\sqrt{2}}{\sqrt{3}}. $ Therefore length of transverse axis of a hyperbola $ =2a=2\times \frac{4\sqrt{2}}{\sqrt{3}}=\frac{8\sqrt{2}}{\sqrt{3}}. $
BETA
