For this question, you will write a program called Circle that displays a circle in the upper right quadrant of the Cartesian plane. To do so, write (at a minimum) the following three methods:

A. A method called onCircle that takes as input five ints. The first three parameters represent (in order) the radius and x,y coordinates of the centre of the circle. The last two parameters represent an x,y position on the grid. This method determines whether or not the circle should be drawn at the grid coordinates given by the method's parameters.

To get the appropriate thickness for the circle, return whether the following formula holds or not: radius2 =(x-a)2 +(y-b)2 =radius2 +1 In the above formula, a and b are the coordinates of the centre of the circle, and x and y are the grid coordinates.

B. A method called verifyInput that takes as input three ints representing the radius and centre coor- dinates of the circle, and returns nothing.

This method should throw an IllegalArgumentException and display a helpful error message if either the circle does not fit in the upper right quadrant, or if the radius is non-positive. Otherwise, the method will not print anything. As a hint, the circle does not fit in the upper-right quadrant if it is too close to the axes.

C. A method called drawCircle that takes as input an int representing the radius of the circle, another int representing the x coordinate of the centre of the circle, and a third int representing the y coordinate of the circle's centre.

It also takes as input a char representing the symbol with which the circle will be drawn. Both of the methods described above must be called and used appropriately in this method in order to get full points. The rules for displaying the axes (the x-axis and the y-axis) are as follows: the minimum length and height of each axis is 9. If the circle fits in the 9 by 9 quadrant, there should be 9 vertical bars (|) representing the y-axis, and 9 horizontal dashes (-) representing the x-axis. You should use the plus symbol (+) to represent the origin.

The y-axis should end in a hat symbol (?), and the x-axis should end in a right triangle bracket (>). This means that there are a total of 11 characters on the x-axis, and 11 on the y-axis, with the origin counting as being on both. If the circle does not fit, the appropriate axis (or axes) should be extended. They still must end in (?) and (>), and the origin remains the same. Sample output for various input values is shown below. Note that, due to rounding errors and display dimensions of characters, the circle will not look like a perfect circle.

This is expected behaviour. If more than one character should be drawn at the same location (eg, if the circle intersects with an axis), the circle gets priority. This is slightly different from what happened in the second warm-up exercise. See the second example below for sample output in this scenario.