If a point P has co-ordinates (0,-2) and Q is any point on the circle, x2+ y2-5x-y+5=0, then the maximum value of (PQ)2 is:

P(0,-2) and Q on circle x²+y²-5x-y+5=0So centre of circle is (5/2 , 1/2)Which can directly find by trick ( general equation of circle is ax²+by²+2gx+2fy+c=0 so centre is (-g/2,-f/2))So farthest point is always perpendicular line so slope of line with point (5/2 , 1/2) and (0,-2) is -1 .So its perpendicular line slope is 1 .So equation of line which is farthest from circle is ( y-0)=1(x+2)= x-y+2 ans

P(0,-2) and Q on circle x²+y²-5x-y+5=0So centre of circle is (5/2 , 1/2)Which can directly find by trick ( general equation of circle is ax²+by²+2gx+2fy+c=0 so centre is (-g/2,-f/2) and radius is (g²+f²-c))So radius is (3/2)½ and total length from center to (0,-2) is. 5/(2)½. So distance PQ is (5 - (3)½)/ (2)½ and max value of (PQ)² is {14 - 5(3)½}.ans