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) \[{{x}^{2}}+4x+{{y}^{2}}-4y+4=0\]
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 \[{{x}^{2}}+{{y}^{2}}-4x-4y+4=0\].
You need to login to perform this action.
You will be redirected in
3 sec
