Given that one focus S = (6, 2), centre C = (1, 2),P = (4, 6)
The other focus S’ = (–4, 2) (since C is the midpoint of SS’)
SS’ = 2ae ⇒ 2ae = 10 ⇒ ae = 5;
SP+S′P=2a⇒2√5+4√5⇒a=3√5⇒a2=45 and b2=a2−a2e2⇒b2=20
∴ Equation of the ellipse is (x−1)245+(y−2)220=1