Question

数学难题，只要第3题。高手进。（注:请用初中方法，但可以用点到直线距离公式，圆方程，两点间距离公式）谢谢。

Answer 1

P(a,0)

|CD|=|CF|=1

y=(1/4)x^2+bx+c

x=0,|OA|=y=c

A(0,c),B(c,c),C(c,0),E(1+c,1),F(1+c,0)

r^2=PA^2=PB^2=PE^2

a=1,c=2

(1)

y=(1/4)x^2-(3/2)x+2

P(1,0),F(3,0),G(4,0),M(3.5,0),C(2,0),|CG|=2

(2)

k(PE)*k(ME)=-1

(3)

N(x,y),C(2,0),G(4,0)

k(NC)=y/(x-2),k(NG)=y/(x-4)

[k(NG)-k(NC)]/[1+k(NG)*k(NC)]≤1/√3

[y/(x-4)-y/(x-2)]/[1+y/(x-4)*y/(x-2)]≤1/√3

2y/(x^2-6x+8+y^2))≤1/√3

y=(1/4)x^2-(3/2)x+2=0.25x^2-1.5x+2

4y=x^2-6x+8

x^2-6x+8=(1/4)y=0.25y

2y/(x^2-6x+8+y^2)

=2y/(4y+y^2)

=2/(4+y)

=2/(4+0.25x^2-1.5x+2)

=8/(24+x^2-6x)

8/(24+x^2-6x))≤1/√3