Circle And System Of Circles Question 331
Question: The pole of the line $ 2x+3y=4 $ w.r.t circle $ x^{2}+y^{2}=64 $ is
[RPET 1996]
Options:
A) (32, 48)
B) (48, 32)
C) (- 32, 48)
D) (48, -32)
Show Answer
Answer:
Correct Answer: A
Solution:
Let pole be $ (x_1,\ y_1) $ . Then the equation of the polar is, $ xx_1+yy_1=a^{2} $
$ \therefore \ xx_1+yy_1=64 $ …………. (i) Since (i) and line $ 2x+3y=4 $ represent the same straight line.
$ \Rightarrow \frac{x_1}{2}=\frac{y_1}{3}=\frac{-64}{-4}\Rightarrow x_1=32,\ y_1=48 $ Trick: Pole $ ( \frac{-la^{2}}{n},\ \frac{-ma^{2}}{n} )\Rightarrow (32,\ 48) $ .
BETA
