The two circles x2+y2−2x+22y+5=0 and x2+y2+14x+6y+k=0 intersect orthogonally provided k is equal to ?
If 2 circles cut each other orthogonally then
d2=r12+r22 where d is the distance between the centers
C1=(1,11), r1=√12+112−5=√117
C2=(−7,−3), r2=√72+32−k=√58−k
(C1C2)2=r12+r22
82+82=117+58−k
129=175−k
⟹k=47