Circle And System Of Circles Question 333
Question: If a line passing through origin touches the circle $ {{(x-4)}^{2}}+{{(y+5)}^{2}}=25 $ , then its slope should be
Options:
A) $ \pm \frac{3}{4} $
B) 0
C) $ \pm ,3 $
D) $ \pm ,1 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let equation of line be $ y=mx $ or $ y-mx=0 $ Then applying condition for tangency, $ | \frac{-5-4m}{\sqrt{1+m^{2}}} |=5\Rightarrow 25+16m^{2}+40m=25+25m^{2} $
$ \Rightarrow 9m^{2}-40m=0\Rightarrow m=0 $ or $ m=\frac{40}{9} $ .
BETA
