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Let C1 and C2 be parabolas x^2 = y - 1 a...

Let `C_1` and `C_2` be parabolas `x^2 = y - 1` and `y^2 = x-1` respectively. Let P be any point on `C_1` and Q be any point `C_2`. Let `P_1` and `Q_1` be the reflection of P and Q, respectively w.r.t the line y = x then prove that `P_1` lies on `C_2` and `Q_1` lies on `C_1` and `PQ >= [P P_1, Q Q_1]`. Hence or otherwise , determine points `P_0` and `Q_0` on the parabolas `C_1` and `C_2` respectively such that `P_0 Q_0 <= PQ` for all pairs of points (P,Q) with P on `C_1` and Q on `C_2`

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