Circle And System Of Circles Question 132
Question: Equation of the circle which touches the lines $ x=0,\ y=0 $ and $ 3x+4y=4 $ is
[MP PET 1991]
Options:
A) $ x^{2}-4x+y^{2}+4y+4=0 $
B) $ x^{2}-4x+y^{2}-4y+4=0 $
C) $ x^{2}+4x+y^{2}+4y+4=0 $
D) $ x^{2}+4x+y^{2}-4y+4=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let centre of circle be (h, k). Since it touches both axes, therefore $ h=k=a. $
Hence equation can be $ {{(x-a)}^{2}}+{{(y-a)}^{2}}=a^{2} $
But it also touches the line $ 3x+4y=4 $ .
Therefore, $ \frac{3a+4a-4}{5}=a\Rightarrow a=2 $
Hence the required equation of circle is
$ x^{2}+y^{2}-4x-4y+4=0 $ .
BETA
