We, have, P(1,k) lies on ellipse 9x2+4y2−18x+16y−11=0 ∴‌‌9+4k2−18+16k−11=0 ⇒‌‌4k2+16k−20=0 ⇒‌‌k2+4k−5=0 ⇒‌‌(k+5)(k−1)=0⇒k=−5,1 ∴P is either (1,−5) or (1,1) Again, equation of ellipse is 9x2+4y2−18x+16y−11=0 ⇒‌‌9(x−1)2+4(y+2)2=36 ⇒‌‌‌