A) \[{{x}^{2}}+{{y}^{2}}+x+y-2=0\]
B) \[{{x}^{2}}+{{y}^{2}}-x+y-2=0\]
C) \[{{x}^{2}}+{{y}^{2}}+x-y-2=0\]
D) None of these
Correct Answer: B
Solution :
Equation of BC (chord of contact) is \[0.x+1.y-(x+0)+2(y+1)+1=0\] or \[-x+3y+3=0\] Equation of circle through B and C i.e., intersection of the given circle and chord of contact is \[({{x}^{2}}+{{y}^{2}}-2x+4y+1)+\lambda (-x+3y+3)=0\]. It passes through \[A(0,\ 1)\], so the equation of the required circle is \[{{x}^{2}}+{{y}^{2}}-x+y-2=0\]. Aliter: Centre of the required circle is mid-point of \[A(0,\ 1)\] and centre of the given circle i.e., \[(1,\ -2)\]. Therefore, centre \[\left( \frac{1}{2},\ -\frac{1}{2} \right)\] and radius \[\sqrt{\frac{5}{2}}\]. Hence the circle is \[{{x}^{2}}+{{y}^{2}}-x+y-2=0\].
You need to login to perform this action.
You will be redirected in
3 sec
