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Let P( , ) be a point on the parabola y2=4x. If P also lies on the chord of the parabola x2=8y whose mid point is (1, 54 ), then ( -28)( -8) is equal to .
192
Chord of x2=8y with mid-point (x1, y1): T=S1
xx1-4(y+y1)=x12-8y1
(x1, y1)= (1, 54 ): x-4y-5=-9 x-4y+4=0
=4 -4 and 2=4 =16 -16
2-16 +16=0 =8 4 3, =28 16 3 (same sign)
( -28)( -8)=( 16 3)( 4 3)=192
Answer: 192
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