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2021 LMT Spring Division A Problem 18

Source:

October 22, 2021

Problem Statement

Points

X

and

Y

are on a parabola of the form

y=\frac{x^2}{a^2}

and

A

is the point

(x, y) = (0, a)

. Assume

XY

passes through

A

and hits the line

y=-a

at a point

B

. Let

\omega

be the circle passing through

(0, -a)

,

A

, and

B

. A point

P

is chosen on

XB=10

such that

PA = 8

. Given that

X

is between

A

and

B

,

AX=2

, and

XB=10

, find

PX \cdot PY

.
Proposed by Kevin Zhao

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