Conic Sections Question 300
Question: What is the equation to circle which touches both the axes and has centre on the line $ x+y=4- $
Options:
A) $ x^{2}+y^{2}-4x+4y+4=0 $
B) $ x^{2}+y^{2}-4x-4y+4=0 $
C) $ x^{2}+y^{2}+4x-4y-4=0 $
D) $ x^{2}+y^{2}+4x+4y-4=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] The equation of circle, which touches both the axes, is given by $ x^{2}+y^{2}-2rx-2ry+r^{2}=0 $ - (i) Now the centre (r, r) of this circle lies on the line $ x+y=4 $
$ r+r=4\Rightarrow r=2 $
$ \therefore $ Put value of r in Eq. (i). We get $ x^{2}+y^{2}-4x-4y+4=0 $ which is required equation of circle,
BETA
