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The ninth grade world junior high school mathematics Olympic competition questions can be done.
Solution: Let the coordinates of A, B and C be (U 1 0), (u2,0) and (0,v) respectively, then: U 1

(1), then u 1, u2 is the root of the equation y = ax 2-2a+4 = 0.

AFBC = AFC AFC

= 1/2(v+ 1)(-u 1)+ 1/2(v+ 1)U2

= 1/2(v+ 1)(U2-u 1)

(u2-u 1)^2=(u2+u 1)^2-4u 1u2

=4-4/a

Therefore: s _ afbc =1/2 (v+1) (4-4/a).

C(0, v) is on a parabola, so: v=4.

Then: s _ afbc =10-10/a =15.

So: a= -2.

The parabola is: y =-2x 2+4x+4.

(2)tan∠PCA=? How did this key condition become blank?

(3) 1) has no graph, so we don't know the position of the N point and the Y axis; 2) What is it? Has the value of changed? How can we solve your problem if you don't give me the research object?