1. choose c,

According to the equation, the focal point f (p/2,0),

Let the straight AB equation be y=kx-kp/2.

By combining AB linear equation with parabolic equation and simplifying it, we can know that the answer is C from Vieta theorem.

2. The locus of the center p of the moving circle is a hyperbola;

Can the moving garden equation be (x-x 1)? +(y+y 1)？ =r？

By using C2 c 1 to circumscribe the motion circle p, we can get the equation:

(r+ 1)？ =(x 1+3)？ +y 1？ ..... one

(r+2)？ =(x 1-3)？ +y 1？ ..... two

Solution: r=-( 12x 1+3)/2.

By bringing r into one of the above formulas, we can get the equations about x 1 and y 1, which just meet the standard equation of hyperbola.