According to question, |PA−PB|=2 ⇒√(x−2)2+(y−3)2−√(x−3)2+(y+2)2=2 ⇒√(x−2)2+(y−3)2=2+√(x−3)2+(y+2)2 On squaring, we get (x−2)2+(y−3)2=4+(x−3)2+(y+2)2 +4√(x−3)2+(y+2)2 ⇒x2+4−4x+y2+9−6y =4+x2+9−6x+y2+4+4y+4 √(x−3)2+(y+2)2 ⇒2x−10y−4=4√(x−3)2+(y+2)2 ⇒x−5y−2=2√(x−3)2+(y+2)2 On squaring, (x−5y−2)2=4[(x−3)2+(y+2)2]