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A conic curve math problem in high school?
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1: The simplified straight line is the right directrix, and it is easy to get C = 4 and A = 6 after simplification.

2. Let E F be (x, y) (-x, 4-y) P(a, b) respectively.

PE*PF=(x-a,y-b)*(-x-a,4-y-b)

= a 2-x 2+4y-4b-y 2+b 2 Next, we get the elimination from the analytic formula of the circle: x 2+y 2 = 4y-3.

=a^2+b^2-(4y-3)+4y-4b

= a 2+b 2-4b+3 Next, use the elliptic analytical formula to solve the elimination: a 2 = 6-3b 2.

The value of =-2b 2-4b+9b is-root 2 to root 2. Let's go to one yuan and get the maximum twice.

B=- 1 to get the maximum value, and substitute it to get 1 1.