|z−(4+8i)|=√2 It is a circle with center (4, 8), radius = √10 |z−(3+5i)|+|z−(5+11i)=4√5 It is an ellipse with focii S(3,5)&S′(5,11) SS′=√4+36⇒√40=2√10 Clearly 4√5>SS′ Center of ellipse (
3+5
2
,
5+11
2
)≡(4,8) coincides with center of circle Now, 2a=4√5 a=2√5 c=√10 b2=20−10=10 b=√10 = radius of circle ∴ ellipse & circle will intersect at end points of minor axis So, 2 points of intersection