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Can someone help me out with the K+1 steps on this question please Prove 12^k >= 5^k + 7^k Thanks

P is (2ap, ap^2) and Q(2aq, aq^2) on x^2=4ay. T is point (a(p+q),apq) and tangents at P and Q meet at 45 degrees. I have proven p - q = 1 + pq but are stuck with this question By evaluating the expression x^2=4ay at T, find the locus of T