Combination with co-ordinate geometry question

[nipukumar]

Circle with center (x,y) and radius r such that r=x+2 or r=y+2 to be constructed in xy-plane. The range of possible x-coordinate is -4<=x<=4 and y-coordinate is -8<=y<6. Given these conditions, how many different circles could be constructed ?

No answer choices given. How to solve this problem ?

[atul.prasad]

I assume that x and y are integers.

in that case there are 9 possible values of x and 15 possible values of y.

So we have 15*9 possible "centers" for this circle.
Now, each of these 135 circles could be of radius x+2 or y+2.

So we have 135*2 = 270, different circles
However, when x = y, the circle with r = x+2 or r=y+2 is same.

So we must count out those circles (since we added them twice above).

So the answer should be 270-9 = 261 (since there are 9 possible values when x=y)

[jnelson0612]

I've just worked this through and agree with atul. Excellent work!