Let point of intersection R(h,k)
mBR=mBP⇒h+2k=2cosα+22sinα⇒h+2k=tan2α
mAR=mAQ⇒h−2k=2cosβ−22sinβ=cosβ−1sinβ=−cot2β
2α−2β=4π
tan(2α−2β)=tan4π=1
1+tan2αtan2βtan2α−tan2β=1
1+(h+2k)(k2−h)h+2k+kh−2=1⇒h+24k(h+2)k2+h2−4=1
4kh2+k2−4=1
x2+y2−4y−4=0