M^2 = 8p and 4+p/2 = 17/4.

The solution is m = 2 or -2, and p = 1/2.

2.

Discuss in two situations:

The slope of (1) MQ exists. If k is not 0, it is set to k..

The MQ equation y-t 2 = k (x-t)

C of equation y = x 2, simultaneous linear equation, x 2-kx+kt-t 2 = 0.

Get q abscissa xQ = k-t

Let n (xn, xn 2), NQ slope kNq = (xq2-xn)/(xq-xn) = xq+xn =-1/k.

xN = - 1/k + t - k

If NM is tangent, kNM = 2XN, MN equation y-xN/2 = 2xn * (x-xn), and M coordinate (xn/2,0).

At the same time XM = t-t 2/k

So 2 * (t-t 2/k) = t-k- 1/k, which is simplified.

k^2 - 2kt + ( 1 - 2t^2) = 0

Discriminant = 4 * (3t 2- 1) > = 0, t>= √3/3, and the minimum value of t is √3/3.

If k is 0, n, Q n and q coincide, this is another point that is inconsistent with n.

(2) If K does not exist, Q does not exist.

Comprehensive (1), (2), the minimum value of t is √3/3.