In the xy- plane, the center of circle P is the point (-5,-4). If circle P has an integer radius and each point lying on the circle P has coordinates ( x,y ) such that, x is less than or equal to zero & y is less than or equal to zero then which of the following represents a possible area of circle P ?

Point P is in the third quadrant and the other conditions also indicate that the whole circle itself is restricted to the third quadrant. So the maximum radius of the circle can be when the circle touches one of the axis (Try to draw it out).

The maximum radius will turn out to be 4. So the maximum area will be 16π.

However, as the question says that P can have co-ordinates (0,0) which would imply that the Radius to be Root 41 & as per the question radius to be 6 or less (any integer). So shouldn’t the answer be choices number 2, 4, 5, & 6 ?

Points of the circle is on (x,y) where x and y should both be non-positive. Implying the whole circle (all of the points on it) should be in the third quadrant

Also, the question states that the circle has integer radius.

So with (-5,-4) as center you can draw a circle of radius 1,2,3… and so on. But there’s an upper limit i.e. if you draw a circle with radius more than 4 (say 5), the top most point of the circle will have a y coordinate of +1, so the point on the circle will lie on the second quadrant which will go against point #2