A(0,-1), B(0, 1), let p be the fixed point on circle c, let D = PA 2+Pb 2, and find the maximum and minimum values of d.

Solution: Let P(3+cosa, 4+ Sina),

d=(3+cosa)^2+(5+sina)^2

+(3+cosa)^2+(3+sina)^2

= 54+ 12 Xhosa+16 Sina

=54+20sin(a+b)，

Where b=arctan(3/4),

The maximum value of ∴d =74 and the minimum value =34.

2. Let any point on the curve be (x, y), then

Root number (x 2+y 2)/root number [(x-a) 2+y 2] = k

Then (x 2+y 2)/[(x-a) 2+y 2] = k 2.

The classification is as follows:

( 1-k^2)*x^2+( 1-k^2)*y^2+2*k^2*x-a^2*k^2=0

Divided into the following situations:

(1) When k=0, the curve is a point (0,0).

(2) When k= 1, the curve equation is X = 1/2 * A 2, and the curve is a straight line parallel to the Y axis X = 1/2A 2.

(3) when 1 >; K>0, the curve equation is [x-k2/(1-k2)] 2+y2 = a2+[k2/(1-k2)] 2, and the curve is a circle;

(4) when k >; At 1, the curve equation is [x-k2/(1-k2)] 2+y2 = [k2/(1-k2)] 2-a2.

Divided into the following situations:

(i) When k 2/( 1-k 2)] 2-a 2 = 0, the curve is a point (k 2/( 1-k 2), 0).

(ii) when k 2/( 1-k 2)] 2-a 2

(iii) when k 2/( 1-k 2)] 2-a 2 >; 0, the curve is a circle.