1. Calculus 四電一甲 95310312 郭子瑄

2. In each part, discribe the family of curves. (a.) (x-a) ^ 2+(y-a ^ 2)^ 2 =1 We can find this is a round parametric equation preface. And the lines of all centres of a circle are a parabola. Centre of a circle (a, a ^ 2),r =1 x=a ; y=a^2 *y=x^2 (Figure.1) Figure.1

3. The centres of the circles of (x-a) ^ 2+(y-a ^ 2)^ 2 =1 are on the parabola y=x^2.

5. (b.) y=a+(x-2a)^2 This is a parabola figure. The acmes lie in (2a, a) Opening upwards, the focus is 1/4. x=2a ; y=a *y=x/2 (Figure.2) Figure.2

6. The acmes of the parabola of y=a+(x-2a)^2 are in the line y=x/2.