Let the centre of circle be (h,k). Here, ‌‌|h|=|k|=r ⇒‌‌h2=k2=r Centre of the circle lies on line x−2y−3=0, ‌h−2k−3=0 ⇒‌‌h=2k+3 Equation of circle is ‌(x−h)2+(y−k)2=r2 ⇒(x−2k−3)2+(y−k)2=k2 Circle passes through (0,k) ‌(2k+3)2+(0)2=k2 ⇒4k2+9+12k=k2⇒3k2+12k+9=0 ⇒k2+4k+3=0⇒k=−1,−3 When k=−1, then h=1 and when k=−3, then h=−3 The values are (1,−1) and (−3,−3). The equation of circles are (x−1)2+(y+1)2=1 or ⇒‌(x+3)2+(y+3)2=32 ‌x2+y2−2x+2y+1=0 or ‌x2+y2+6x+6y+9=0