Conic Sections Question 201
Question: The length of the axes of the conic $ 9x^{2}+4y^{2}-6x+4y+1=0 $ , are
[Orissa JEE 2002]
Options:
A) $ \frac{1}{2},\ 9 $
B) $ 3,\ \frac{2}{5} $
C) $ 1,\ \frac{2}{3} $
D) 3, 2
Show Answer
Answer:
Correct Answer: C
Solution:
Given that, the equation of conic $ 9x^{2}+4y^{2}-6x+4y+1=0 $
therefore $ {{(3x-1)}^{2}}+{{(2y+1)}^{2}}=1 $
therefore $ \frac{{{( x-\frac{1}{3} )}^{2}}}{\frac{1}{9}}+\frac{{{(y+1)}^{2}}}{\frac{1}{2}}=1 $ . Here $ a=\frac{1}{3} $ , $ b=\frac{1}{2} $ ; $ 2a=\frac{2}{3} $ , $ 2b=1. $
Length of axes are $ ( 1,\frac{2}{3} ) $ .
BETA
