Solution: According to the meaning of the question, the focus F(0, p/2) is a symmetrical point; Display midpoint coordinates (MX+NX)/2 = 0...(I), (My+NY)/2 = P/2 ... (ii);

Tangent line intersects with point D (0,-1/2); According to the symmetry of C about Y axis, we know that the linear equation of My = NyMD is: (Y+1/2)/X = (My+1/2)/MX, and Y = (P/2+1/2) X/MX-/. Similarly, the equation of ND is: y =-(p/2+1/2) x/MX-1/2 ... iv; Substituting (iii) into the parabolic equation, we get: mx2 = 2p * [(p+1) mx/2mx-1/2 = p2 = p2+p-1/2; Mx=-√(p^2+p- 1/2)、nx=√(p^2+p- 1/2)； Substitution into (iv) gives:

p/2=-(p/2+ 1/2)√(p^2+p- 1/2)/[-√(p^2+p- 1/2)]- 1/2=-p/2- 1； Solution: p= 1.

The equation of parabola c is: x 2 = 2y.