MathDB

A18

Part of 2021 LMT Spring

Problems(1)

2021 LMT Spring Division A Problem 18

Source:

10/22/2021
Points XX and YY are on a parabola of the form y=x2a2y=\frac{x^2}{a^2} and AA is the point (x,y)=(0,a)(x, y) = (0, a). Assume XYXY passes through AA and hits the line y=−ay=-a at a point BB. Let ω\omega be the circle passing through (0,−a)(0, -a), AA, and BB. A point PP is chosen on ω\omega such that PA=8PA = 8. Given that XX is between AA and BB, AX=2AX=2, and XB=10XB=10, find PX⋅PYPX \cdot PY.
Proposed by Kevin Zhao