Duration: 8:24

29 views

0

Let \( C_{1} \) and \( C_{2} \) be respectively, the parabolas \( x^{2}=y-1 \) and \( y^{2}=x-1 \). Let \( P \) be any point on \( C_{1} \) and \( Q \) be any
P point on \( C_{2} \). If \( P_{1} \) and \( Q_{1} \) is the reflections of \( P \) and \( Q \),

W respectively, with respect to the line \( y=x \). Prove that \( P_{1} \) lies on \( C_{2} Q_{1} \) lies on \( C_{1} \) and \( P Q \geq \min \left(P P_{1}, Q Q_{1}\right) \). Hence, determine points \( P_{0} \) and \( Q_{0} \) on the parabolas \( C_{1} \) and \( C_{2} \) respectively such that \( P_{0} Q_{0} \leq P Q \) for all pairs of points \( (P, Q) \) with \( P \) on \( C_{1} \) and \( Q \) on \( C_{2} \).
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live