Question 1 in Java (Geometry: the Circle2D class) Define the Circle2D class that contains:

1) Two double data fields named x and y that specify the center of the circle with getter methods.

2) A data field radius with a getter method.

3) A no-arg constructor that creates a default circle with (0, 0) for (x, y) and 1 for radius.

4) A constructor that creates a circle with the specified x, y, and radius.

5) A method getArea() that returns the area of the circle.

6) A method getPerimeter() that returns the perimeter of the circle.

7) A method contains(double x, double y) that returns true if the specified point (x, y) is inside this circle (see Figure a).

8) A method contains(Circle2D circle) that returns true if the specified circle is inside this circle (see Figure b).

9) A method overlaps(Circle2D circle) that returns true if the specified circle overlaps with this circle (see Figure c).

Figure above (a) A point is inside the circle. (b) A circle is inside another circle. (c) A circle overlaps another circle.

Write a test program that creates a Circle2D object c1 (new Circle2D(2, 2, 5.5)), displays its area and perimeter, and displays the result of c1.contains(3, 3), c1.contains(new Circle2D(4, 5, 10.5)), and c1.overlaps(new Circle2D(3, 5, 2.3)).

Question 2 in Java

Approximate e using the following series:

In order to get better precision, use BigDecimal with 25 digits of precision in the computation.

Write a program that displays the e value for i = 100, 200, . . . , and 1000.

(a) (b) e=1+1!1+2!1+3!1+4!1++i!1