Let P(t12,2t1) and Q(t22,2t2) are extremetre of chord ∴h=43t12+t22,k=46t1+2t2
Slope of PQ=2 ∴2=t12−t222t1−2t2 t1+t2=1 ⇒t2=1−t1
Put the value of t2 in h and k, we get 4h=3t12+(1−t1)2,4k=6t1+2−2t1 4h=4t12−2t1+1,4k=4t1+2
Eliminating t1, we get 4h=4(22k−1)2−2(22k−1)+1 4h=4k2−6k+3 ⇒(k−43)2=4(h−163) ∴ Vertex (163,43)